WASHINGTON — President Trump pushed his lawyers in recent days to try once again to reach an agreement with the special counsel’s office about him sitting for an interview, flouting their advice that he should not answer investigators’ questions, three people briefed on the matter said on Wednesday.
Mr. Trump has told advisers he is eager to meet with investigators to clear himself of wrongdoing, the people said. In effect, he believes he can convince the investigators for the special counsel, Robert S. Mueller III, of his belief that their own inquiry is a “witch hunt.”
Mr. Mueller, whose team has negotiated the parameters of an interview with Mr. Trump’s lawyers for eight months, sent his latest proposal in a letter Tuesday night, the three people said. Investigators stood firm on the scope of and topics for their questions for Mr. Trump: possible coordination between his associates and Russia’s election interference and whether he tried to obstruct the investigation.
They did shift slightly on format, agreeing to accept some written answers, including matters in which they want to preserve the ability to have Mr. Trump answer follow-ups in person. In doing so, they firmed up a previously expressed willingness to allow certain answers in writing.
The president’s lawyers are unwilling to concede to follow-ups in person, citing concerns that Mr. Trump will increase his legal exposure, the people said. They have been prepared to tell Mr. Mueller’s office there will be no interview, risking a court fight over a subpoena that could drag into November’s midterm elections, but Mr. Trump pushed them to continue negotiating. The lawyers are likely to counter Mr. Mueller’s proposal in the coming days, according to the three people.
“We’re in the process of responding to their proposal,” the president’s lead lawyer for the investigation, Rudolph W. Giuliani, told reporters after an event in Portsmouth, N.H., on Wednesday. The special counsel’s office declined to comment.
The monthslong back and forth among the special counsel’s office, Mr. Trump’s lawyers and the president himself demonstrates the significant obstacles that still stand in the way of an interview. Mr. Trump has put his lawyers in the vexing position of trying to follow the desires of their client while seeking to protect him from legal jeopardy at the same time.
Mr. Trump’s belief that an interview would bring the investigation to a swift end ignores several realities: that the investigation sprawls into areas well beyond his behavior; the possibility that Justice Department officials will hand over the results of the investigation to lawmakers to decide whether to proceed, thus prolonging the inquiry; and the lack of any public indication from the special counsel about how much work he has ahead of him.
If Mr. Trump ultimately decides to refuse to voluntarily be interviewed, he could sustain some political damage as he would be forced to explain to the public why he cannot answer the special counsel’s questions if he did nothing wrong.
Mr. Trump believes that he needs a daily drumbeat of criticisms against the investigation in order to sway public opinion in his favor. His lawyers have told him he has no personal legal exposure and that the only threat to him would be impeachment proceedings if the Democrats win control of the House in November.
Mr. Mueller remains interested in key areas Mr. Trump’s lawyers worry will prove problematic for him, particularly whether he obstructed justice when he fired James B. Comey as the F.B.I. director. Mr. Comey has testified the president pressured him to drop an investigation into his first national security adviser, Michael T. Flynn.
Legal experts and law enforcement officials who have worked with Mr. Mueller have said that they believe he would pursue all available avenues to get Mr. Trump to answer questions about his conduct and try to determine his intent. Mr. Trump’s lawyers, however, remain unconvinced that Mr. Mueller would risk losing a subpoena fight in court.
For the past week, Mr. Trump has expressed frustration about the confluences of investigations that have dogged him. The president told his advisers that the Russia inquiry and a separate federal investigation in Manhattan into his former personal lawyer, Michael D. Cohen, have undermined him for too long and need to be brought to an end.
The president’s concerns were reignited by both the start of the money fraud trial of his former campaign chairman, Paul Manafort, and the release last week of a recording on which he and Mr. Cohen are heard discussing hush money payments during the campaign to a former Playboy model who says she had an affair with Mr. Trump. He denies the affair.
On Wednesday morning, those frustrations burst into public view. Mr. Trump fired off a string of tweets, including a call for Attorney General Jeff Sessions to end Mr. Mueller’s investigation.
“This is a terrible situation and Attorney General Jeff Sessions should stop this Rigged Witch Hunt right now, before it continues to stain our country any further,” Mr. Trump wrote. He ignored that Mr. Sessions has recused himself from the investigation, which is overseen by the deputy attorney general, Rod J. Rosenstein.
Michael S. Schmidt reported from Washington, and Maggie Haberman from New York.