And though the Trump administration has said Mr. Page was a bit player who had no access to the candidate, the wiretap shows the F.B.I. had strong evidence that a campaign adviser was operating on behalf of Moscow.
Both Mr. Trump and Mr. Page have called the investigation a “witch hunt” and said it was cooked up by their political rivals for speaking out against President Barack Obama’s policies. On Tuesday, Mr. Page said in an email that it “will be interesting to see what comes out when the unjustified basis for those FISA requests are more fully disclosed over time,” using shorthand for the court.
The F.B.I. declined to comment. James B. Comey, the F.B.I. director, has described the hurdles to obtaining an intelligence wiretap as a “rigorous, rigorous process.”
The wiretap of Mr. Page was reported by The Washington Post. The revelation followed months of speculation about such warrants against associates of Mr. Trump, an idea that was broached in November by Heat Street, a news and entertainment website that cited a pair of unnamed sources with “links to the counterintelligence community” in its report. Heat Street was founded by Louise Mensch, a former Conservative member of the British Parliament who emerged as a fierce critic of Mr. Trump, and it is owned by Rupert Murdoch’s News Corporation, which publishes The Wall Street Journal and The Times of London.
The official who confirmed the warrant against Mr. Page did so on the condition of anonymity because intelligence wiretaps are classified.
The official was not aware of any instances in which an active member of Mr. Trump’s campaign was directly surveilled by American law-enforcement or spy agencies, though some Trump associates were swept up in surveillance of foreign officials.
That assertion was in line with previous statements by Obama administration officials, including James R. Clapper Jr., the former director of national intelligence, who said during a March 5 appearance on NBC’s “Meet the Press” that the surveillance court issued no warrants either for the president or his campaign staff.
“For the part of the national security apparatus that I oversaw as D.N.I., there was no such wiretap activity mounted against the president-elect at the time, or as a candidate, or against his campaign,” Mr. Clapper said.
As part of the investigation, American intelligence agencies have examined wiretapped communications and phone records. Among those intercepts were conversations among Kremlin officials about contacts with people close to Mr. Trump, including Mr. Page, according to current and former American security officials.
A spokesman for Mr. Clapper did not respond for requests for comment. A spokesman for the Office of the Director of National Intelligence declined to comment.
Mr. Page, a former Moscow-based investment banker for Merrill Lynch who later founded an investment company in New York called Global Energy Capital, has been on the F.B.I.’s radar screen for years.
In early 2013, he met with a Russian intelligence officer posing as a banker in New York. The Russian agent was part of an espionage ring the F.B.I. had been investigating, and court records indicate that the spy tried to recruit Mr. Page.
That year, the F.B.I. interviewed Mr. Page, who said he did not know he had met with a Russian intelligence officer.
Last July, while working as an adviser to Mr. Trump, who accepted the Republican nomination for president later that month, Mr. Page traveled to Moscow and criticized American foreign policy toward Russia in a speech at the New Economic School, a university.
The address in Moscow and Mr. Page’s contacts with Russians raised alarm bells anew within the F.B.I.
Later that month, the agency opened its counterintelligence investigation into whether any of Mr. Trump’s associates had colluded with Russians to influence the election.
Late last year after the election, Mr. Page traveled to Moscow again and said he was there to meet with “business leaders and thought leaders.” Former and current federal investigators say he would most likely have remained of interest to Russian intelligence because of his links to the Trump administration.
Mr. Page said on CNN on Wednesday that he was not a foreign agent. “Until there’s full evidence and a full investigation has been done, we just don’t know,” Mr. Page said. He repeatedly declined to answer questions about whether he had been interviewed by the F.B.I., adding that he had “nothing to say about any ongoing investigations.”
The probe has been a political distraction for the Trump administration since before Inauguration Day. After denying that any of his associates had Russian contacts, Mr. Trump saw a steady string of news accounts revealing such encounters. His national security adviser, Michael T. Flynn, was forced to resign over misleading comments he made about his conversations with the Russian ambassador to the United States, Sergey I. Kislyak. And Attorney General Jeff Sessions, who also advised Mr. Trump’s campaign, recused himself from the Justice Department investigation in response to questions about his own contacts with Mr. Kislyak.
According to court records, Mr. Page had been looking to make money in Russia, and Russia’s Foreign Intelligence Service singled him out. The F.B.I. secretly recorded Russian spies talking about Mr. Page, describing him as an enthusiastic “idiot.”
The F.B.I. has also been investigating Paul Manafort, Mr. Trump’s former campaign chairman, who is accused of taking millions of dollars in secret payments from a pro-Russian party in Ukraine. He has denied wrongdoing.
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