But a senior White House official said that Donald F. McGahn II, the president’s chief counsel, was working to secure access to what Mr. McGahn believed to be an order issued by the Foreign Intelligence Surveillance Court authorizing some form of surveillance related to Mr. Trump and his associates.
The official offered no evidence to support the notion that such an order exists. It would be a highly unusual breach of the Justice Department’s traditional independence on law enforcement matters for the White House to order it to turn over such an investigative document.
Any request for information from a top White House official about a continuing investigation would be a stunning departure from protocols intended to insulate the F.B.I. from political pressure. It would be even more surprising for the White House to seek information about a case directly involving the president or his advisers, as does the case involving the Russia contacts.
Last month, Reince Priebus, the White House chief of staff, came under fire for asking a top F.B.I. official to publicly rebut news reports about contacts between Trump campaign officials and the Russian government.
Sean Spicer, the White House press secretary, said in a statement that the “White House counsel is reviewing what options, if any, are available to us.” Mr. McGahn did not respond to a request for comment.
The president’s decision on Saturday to lend the power of his office to accusations against his predecessor of politically motivated wiretapping — without offering any proof — was remarkable, even for a leader who has repeatedly shown himself willing to make assertions that are false or based on dubious sources.
It would have been difficult for federal agents, working within the law, to obtain a wiretap order to target Mr. Trump’s phone conversations. It would have meant that the Justice Department had gathered sufficient evidence to convince a federal judge that there was probable cause to believe Mr. Trump had committed a serious crime or was an agent of a foreign power, depending on whether it was a criminal investigation or a foreign intelligence one.
Former officials pointed to longstanding laws and procedures intended to ensure that presidents cannot wiretap a rival for political purposes.
“A cardinal rule of the Obama administration was that no White House official ever interfered with any independent investigation led by the Department of Justice,” said Kevin Lewis, a spokesman for Mr. Obama. “As part of that practice, neither President Obama nor any White House official ever ordered surveillance on any U.S. citizen.”
Mr. Trump asserted just the opposite in a series of five Twitter messages beginning just minutes before sunrise in Florida, where the president is spending the weekend at his Mar-a-Lago estate.
In the first message, the president said he had “just found out” that “Obama had my ‘wires tapped’ in Trump Tower” before the election. Mr. Trump’s reference to “wires tapped” raised the possibility that he was referring to some other type of electronic surveillance and was using the idea of phone tapping loosely.
Two people close to Mr. Trump said they believed he was referring to a Breitbart News article, which aides said had been passed around among his advisers. Mark Levin, a conservative radio host, had also embraced the theory recently in a push against what right-leaning commentators have been calling the “deep state.”
The Breitbart article, published on Friday, claimed that there was a series of “known steps taken by President Barack Obama’s administration in its last months to undermine Donald Trump’s presidential campaign and, later, his new administration.” Stephen K. Bannon, Mr. Trump’s chief strategist, once led Breitbart News.
If Mr. Trump was motivated to take to Twitter after reading the Breitbart article or listening to Mr. Levin, he was using a presidential megaphone to spread dark theories of a broad conspiracy aimed at undermining his presidential ambitions, and later his presidency.
Even with the Breitbart article circulating, several of Mr. Trump’s advisers were stunned by the president’s morning Twitter outburst. Those advisers said they were uncertain about what specifically Mr. Trump was referring to; one surmised that he may also have been referring to a months-old news report about a secret surveillance warrant for communications at his New York offices.
One senior law enforcement official from the Obama administration, who has direct knowledge of the F.B.I. investigation into Russia and of government wiretapping, said that it was “100 percent untrue” that the government had wiretapped Mr. Trump. The official, who asked for anonymity to discuss matters related to investigations and intelligence, said the White House owed the American people an explanation for the president’s allegations.
Ben Rhodes, a former top national security aide to Mr. Obama, said in a Twitter message directed at Mr. Trump on Saturday that “no president can order a wiretap” and added, “Those restrictions were put in place to protect citizens from people like you.”
The House and Senate Intelligence Committees are moving forward with their own investigations into Russia’s efforts to influence the election, and they have said they will examine links between Mr. Trump’s associates and the Russians.
Senator Chris Coons, Democrat of Delaware, said on Friday that he believed there were “transcripts” that would help document those contacts, though he said he had not yet seen them.
“There are transcripts that provide very helpful, very critical insights into whether or not Russian intelligence or senior Russian political leaders — including Vladimir Putin — were cooperating, were colluding, with the Trump campaign at the highest levels to influence the outcome of our election,” Mr. Coons told Andrea Mitchell on MSNBC. “I believe they exist.”
In a written statement on Saturday, a spokesman for Mr. Coons said that the senator “did not imply that he is aware of transcripts indicating collusion between the Trump campaign and the Russians.” The spokesman, Sean Coit, said Mr. Coons had “simply stated that a full review of all relevant transcripts and intelligence intercepts is necessary to determine if collusion took place.”
The New York Times reported in January that among the associates whose links to Russia are being scrutinized are Paul Manafort, Mr. Trump’s onetime campaign chairman; Carter Page, a businessman and foreign policy adviser to the campaign; and Roger Stone, a longtime Republican operative who said he was in touch with WikiLeaks at one point before it released a trove of emails from John D. Podesta, Hillary Clinton’s campaign chairman, last August. Mr. Stone later said he had communicated with WikiLeaks through an intermediary.
Mr. Trump appeared on Saturday to suggest that warrants had been issued by the Foreign Intelligence Surveillance Court. He claimed that the Obama administration had once been “turned down by court” in its supposed efforts to listen in on conversations by Mr. Trump and his associates.
In the fall, the F.B.I. examined computer data showing an odd stream of activity between a Trump Organization server and Alfa Bank, one of Russia’s biggest banks, whose owners have longstanding ties to Mr. Putin. While some F.B.I. officials initially believed that the computer activity indicated an encrypted channel between Moscow and New York, the bureau ultimately moved away from that view. The activity remains unexplained.
There is no confirmed evidence that the F.B.I. obtained a court warrant to wiretap the Trump Organization or was capturing communications directly from the Trump Organization.
During the transition, the F.B.I. — which uses FISA warrants to eavesdrop on the communications of foreign leaders inside the United States — overheard conversations between the Russian ambassador to the United States and Michael T. Flynn, whom Mr. Trump had named national security adviser.
Mr. Trump has pointedly and repeatedly questioned in conversations how it was that Mr. Flynn’s conversations were recorded, and wondered who could have issued a warrant.
After The Washington Post reported that Mr. Flynn and the ambassador, Sergey I. Kislyak, had discussed sanctions that the Obama administration had just imposed on Russia, Mr. Flynn was pushed out of his post by the White House because he had lied to Vice President Mike Pence about the nature of the calls.
The Breitbart article cited mainstream news reports and concluded — going beyond the public record — that the Obama administration had “obtained authorization to eavesdrop on the Trump campaign; continued monitoring the Trump team even when no evidence of wrongdoing was found; then relaxed the N.S.A. rules to allow evidence to be shared widely within the government.”
Mr. Levin, a day earlier, railed about what he called a “much bigger scandal,” claiming — again with no proof — that Mr. Obama and his aides had used “the instrumentalities of the federal government, intelligence activity, to surveil members of the Trump campaign and put that information out in the public.”
Several senior members of Mr. Trump’s White House staff, including his spokesman, Sean Spicer, did not respond to an email requesting on-the-record responses to more than a half-dozen questions about Mr. Trump’s Twitter posts.
Representative Adam B. Schiff, the top Democrat on the House Intelligence Committee, denounced the “willingness of the nation’s chief executive to make the most outlandish and destructive claims without providing a scintilla of evidence to support them.”
Even some Republican lawmakers questioned Mr. Trump’s accusations. Senator Ben Sasse of Nebraska issued a statement demanding that the president reveal everything he knows about any wiretaps or warrants.
“The president today made some very serious allegations, and the informed citizens that a republic requires deserve more information,” Mr. Sasse said, adding that “we are in the midst of a civilization-warping crisis of public trust.”
Taping calls seems to hold a spot in Mr. Trump’s consciousness. He spent many years taping his own phone calls as a businessman. During the campaign, Mr. Trump’s staff members told reporters they feared that their offices were being bugged.
But Mr. Trump’s latest allegations represented a sharp change in his tone toward Mr. Obama.
The current president has frequently spoken about how much he admires Mr. Obama for the gracious way he handled the transition. But since taking office, Mr. Trump has frequently clashed with the intelligence agencies over the Russia inquiries, including efforts to examine the attempts by that country to influence the presidential election and the contacts between Mr. Trump’s aides and the Russian government.
In recent days, the president has appeared increasingly angry about leaks of information that he believes are coming from law enforcement and intelligence officials who are holdovers or recently departed from Mr. Obama’s administration.
People close to Mr. Trump have described him as determined to stop those people from sabotaging his administration. One adviser said on Friday that the president had been discussing a possible plan to try to prevent leaks from occurring. The adviser declined to elaborate on what the plan might entail.
Two senior administration officials said Mr. Trump had tried for two days to find a way to be on an offensive footing against the news articles resulting from leaks; one person close to Mr. Trump said his explosive claim was a result of that.
Mr. Trump’s mood was said to be volatile even before he departed for his weekend in Florida, with an episode in which he vented at his staff. The president’s ire was trained in particular on Mr. McGahn, his White House counsel, according to two people briefed on the matter.
Mr. Trump was said to be frustrated about the decision by Jeff Sessions, his attorney general, to recuse himself from participating in any investigations of connections between the Trump campaign and Russia. Mr. Trump has said there were no such connections. Mr. Trump, who did not learn that Mr. Sessions was recusing himself until after the decision was made, told aides that it gave an opening to his critics on the Russia issue.
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