President Trump’s personal lawyer on Monday walked back the timeline he had offered a day earlier on when negotiations ended with Russian officials about a proposed Trump Tower project in Moscow, calling his comments “hypothetical” and not intended to convey facts.The latest statement from the lawyer, Rudolph W. Giuliani, was described as a clarification of remarks he made to The New York Times in an interview on Sunday, as well as other remarks he made in interviews on Sunday television news shows.Mr. Giuliani originally quoted Mr. Trump as telling him the negotiations over a Moscow skyscraper continued through “the day I won.” He also said that the president recalled “fleeting conversations” about the deal after the Trump Organization signed a letter of intent to pursue it.The confusion centers on how long Mr. Trump may have known of — or was apprised of — discussions about the Moscow tower proposal, which were led by his former personal lawyer and fixer, Michael D. Cohen.The timeline of negotiations for the skyscraper is important because it shows that Mr. Trump’s company was involved in talks with an American adversary for a business deal through the general election, as he was demanding that President Barack Obama lift sanctions against Russia and urging its government to reveal emails from Hillary Clinton, the Democratic presidential nominee.Even before the uproar over his comments, Mr. Giuliani told The Times that there were no call logs or annotations about conversations on the Moscow project that would provide accurate dates, and he described the president’s legal team as at Mr. Cohen’s “mercy.” As a result, he said, there could have been discussions to emerge later that Mr. Trump did not immediately recall.On Sunday, Mr. Giuliani told The Times that Mr. Trump had said the discussions around the proposed tower were “going on from the day I announced to the day I won.” In television interviews the same day, he said that discussions about the tower might have continued up until November 2016 — the month Mr. Trump was elected president.But on Monday, Mr. Giuliani, in a widely issued statement, said that he was making hypothetical remarks.“My recent statements about discussions during the 2016 campaign between Michael Cohen and then-candidate Donald Trump about a potential Trump Moscow ‘project’ were hypothetical and not based on conversations I had with the president,” Mr. Giuliani said.“My comments did not represent the actual timing or circumstances of any such discussions,” he added. “The point is that the proposal was in the earliest stage and did not advance beyond a free nonbinding letter of intent.”Mr. Cohen pleaded guilty late last year to lying to Congress about the duration of the Moscow proposal; he had indicated initially that it stopped in January 2016.It was not the first time Mr. Giuliani has reversed himself in his comments about issues related to the investigation of Russian election interference that is being led by the special counsel, Robert S. Mueller III.Last week, Mr. Giuliani backtracked from another surprising assertion that left open the possibility that Trump campaign aides might have coordinated with Russia in its election interference in 2016.“There was no collusion by President Trump in any way, shape or form,” Mr. Giuliani said in a statement on Thursday, reiterating the president’s longstanding defense against accusations that his campaign secretly coordinated with Moscow to help swing the election. “Likewise, I have no knowledge of any collusion by any of the thousands of people who worked on the campaign.”He added, referring to discredited conspiracy theories that the president and his allies have long cited, “The only knowledge I have in this regard is the collusion of the Clinton campaign with Russia, which has so far been ignored.”A day earlier, Mr. Giuliani stopped short of defending Trump campaign aides, drawing speculation that he might have inside knowledge of possible coordination with Russia.“I never said there was no collusion between the campaign or between people in the campaign,” he told CNN. He added: “I said the president of the United States. There is not a single bit of evidence the president of the United States committed the only crime you could commit here, conspired with the Russians to hack” the Democratic National Committee.When Mr. Giuliani was hired last April as the public face of Mr. Trump’s legal team, it was part of a strategy to be more aggressive in fighting back against Mr. Mueller. Some of the president’s closest allies believe that Mr. Giuliani was effective in helping change public opinion about the special counsel investigation — at least to some extent.Since then, however, Mr. Giuliani’s statements have included criticisms of the federal prosecutor’s office in Manhattan that he once led. That office, in the Justice Department’s Southern District of New York, last year secured guilty pleas by Mr. Cohen to a series of crimes, including a campaign finance-related charge that implicated Mr. Trump.Several people close to Mr. Trump have grown exasperated with Mr. Giuliani’s public appearances. They also expressed concern that he is increasing prosecutors’ anger with the president and potentially creating a misimpression about the Trump Tower project in Moscow.Mr. Giuliani’s appearances on the Sunday news shows followed an article on the website Buzzfeed last Friday, which reported that Mr. Mueller had amassed evidence that Mr. Trump “personally directed” Mr. Cohen to lie to Congress about the amount of time that the Moscow proposal was active.The special counsel’s office made the rare move of issuing a public statement about the article after it was published, calling it “inaccurate.”A person familiar with the discussions said that Mr. Trump’s lawyers sent a letter to the special counsel earlier in the day on Friday asking for a clarification. By then, several Democrats had discussed the prospect of moving ahead with impeachment proceedings if the article was true, creating a heightened degree of pressure on Mr. Mueller’s team.Democrats in Congress are preparing for the possibility of an impeachment case against Mr. Trump once Mr. Mueller completes his work. In the meantime, Mr. Cohen is scheduled to testify before Congress in an open hearing on Feb. 7.Since that date was announced, Mr. Trump has repeatedly urged prosecutors and the media to investigate Mr. Cohen’s family. Lanny Davis, a spokesman for Mr. Cohen, has said his client fears for his safety and the safety of his family amid those threats.