The author of the memos is Christopher Steele, a former British intelligence officer with MI-6, who once served in Moscow. After Mr. Steele retired in 2009, he founded a private firm called Orbis Business Intelligence in London. Former C.I.A. officials described him as an expert on Russia who is well respected in the spy world.
On Tuesday night, Mr. Trump responded to the memos on Twitter:
In an appearance recorded for NBC’s “Late Night With Seth Meyers,” Mr. Trump’s spokeswoman, Kellyanne Conway, said of the claims in the opposition research memos, “He has said he is not aware of that.”
On Wednesday, a spokesman for President Vladimir V. Putin of Russia dismissed the allegations. “The Kremlin has no compromising dossier on Trump, such information isn’t consistent with reality and is nothing but an absolute fantasy,” the spokesman, Dmitri S. Peskov, said at a news conference.
Since the intelligence agencies’ report on Friday that Mr. Putin of Russia had ordered the hacking and leaks of Democratic emails in order to hurt his Democratic opponent, Hillary Clinton, and help Mr. Trump, the president-elect and his aides have said that Democrats are trying to mar his election victory.
The decision of top intelligence officials to give the president, the president-elect and the so-called Gang of Eight — Republican and Democratic leaders of Congress and the intelligence committees — what they know to be unverified, defamatory material was extremely unusual.
The appendix summarized opposition research memos prepared mainly by a retired British intelligence operative for a Washington political and corporate research firm. The firm was paid for its work first by Mr. Trump’s Republican rivals and later by supporters of Mrs. Clinton. The Times has checked on a number of the details included in the memos but has been unable to substantiate them.
The memos suggest that for many years, the Russian government of Mr. Putin has looked for ways to influence Mr. Trump, who has traveled repeatedly to Moscow to investigate real estate deals or to oversee the Miss Universe competition, which he owned for several years. Mr. Trump never completed any major deals in Russia, though he discussed them for years.
Mr. Steele, who gathered the material about Mr. Trump, is considered a competent and reliable operative with extensive experience in Russia, American officials said. But he passed on what he heard from Russian informants and others, and what they told him has not yet been vetted by American intelligence.
The memos describe sex videos involving prostitutes with Mr. Trump in a 2013 visit to a Moscow hotel. The videos were supposedly prepared as “kompromat,” or compromising material, with the possible goal of blackmailing Mr. Trump in the future.
The memos also suggest that Russian officials proposed various lucrative deals, essentially as disguised bribes in order to win influence over Mr. Trump.
The memos describe several purported meetings during the 2016 presidential campaign between Trump representatives and Russian officials to discuss matters of mutual interest, including the Russian hacking of the Democratic National Committee and Mrs. Clinton’s campaign chairman, John D. Podesta.
If some of the unproven claims in the memos are merely titillating, others would amount to extremely serious, potentially treasonous acts.
One of the opposition research memos quotes an unidentified Russian source as claiming that the hacking and leaking of Democratic emails was carried out “with the full knowledge and support of TRUMP and senior members of his campaign team.” In return, the memo said, “the TRUMP team had agreed to sideline Russian intervention in Ukraine as a campaign issue” because Mr. Putin “needed to cauterize the subject.”
Michael Cohen, a lawyer and adviser to Mr. Trump, also went to Twitter to deny a specific claim in the opposition research involving him. One of the memos claims that Mr. Cohen went to Prague in August or September to meet with Kremlin representatives and to talk about Russian hacking of Democrats.
Mr. Cohen tweeted on Tuesday night:
In addition, in a recent interview with The Times, one of the Russian officials named in the memo as having met with Mr. Cohen, Oleg Solodukhin, denied that he had met with Mr. Cohen or any other Trump representative.
“I don’t know where that rumor came from,” Mr. Solodukhin, of the Russian organization Rossotrudnichestvo, which promotes Russian culture and interests abroad, said in a telephone interview.
The Times reported before the election that the F.B.I. was looking into possible evidence of links between the Trump campaign and Russia. But the investigation surfaced again at a Senate hearing on Tuesday in a series of questions from Senator Ron Wyden, Democrat of Oregon, to the F.B.I. director, James B. Comey.
Mr. Wyden, trying to draw Mr. Comey out on information he may have heard during a classified briefing, asked if the F.B.I. had investigated the Trump campaign’s contacts with Russia. Mr. Comey demurred, saying he could not discuss any investigations that might or might not be underway. Mr. Wyden kept pressing, asking Mr. Comey to provide a written answer to the question before Mr. Trump’s inauguration on Jan. 20 because he feared there would be no declassification of the information once Mr. Trump took office.
After the hearing, Mr. Wyden posted on Twitter:
The F.B.I. obtained the material long before the election, and some of the memos in the opposition research dossier are dated as early as June. But agents have struggled to confirm it, according to federal officials familiar with the investigation.
Allies of Senator Harry Reid, the Senate Democratic leader from Nevada who retired at the end of the year, said the disclosures validated his call last summer for an investigation by the F.B.I. into Mr. Trump’s links to Russia.
Democrats on Tuesday night pressed for a thorough investigation of the claims in the memos. Representative Eric Swalwell of California, a member of the House Intelligence Committee, called for law enforcement to find out whether the Russian government had had any contact with Mr. Trump or his campaign.
“The president-elect has spoken a number of times, including after being presented with this evidence, in flattering ways about Russia and its dictator,” Mr. Swalwell said. “Considering the evidence of Russia hacking our democracy to his benefit, the president-elect would do a service to his presidency and our country by releasing his personal and business income taxes, as well as information on any global financial holdings.”
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