President Donald Trump's attorney Rudy Giuliani on Wednesday called on special counsel Robert Mueller to conclude his probe "without further delay" shortly after responding to Mueller's latest proposal to have his investigators interview the president.
Giuliani rejected Mueller's terms, The New York Times reported, citing people familiar with the matter. While Giuliani has not detailed his specific objections, Trump's attorneys do not want the president discussing possible obstruction, for fear that he may perjure himself, according to the newspaper's report.
Negotiations between the president and the special counsel have crept apace for eight months with little apparent progress, raising the specter that Mueller will seek a subpoena for Trump's testimony. Mueller threatened to subpoena the president in March, The Washington Post reported earlier this year.
Trump's attorneys have said they would take a subpoena fight to court, which could set the stage for a high-stakes legal battle between the special counsel and the president that would almost certainly end up at the Supreme Court.
"I think both sides have a big incentive to reach some sort of agreement in setting out the parameters of a voluntary interview," said Joseph Moreno, a former federal prosecutor and a partner at the law firm Cadwalader.
Moreno said that if it comes down to a subpoena fight, Mueller would likely win, but the process would prolong the investigation considerably. But it is a legal remedy he would likely pursue if given no other options.
"Bob Mueller is really tough, and he is not going to be boxed in whether it is by [limits on potential] questions or by time or any other ridiculous parameters," Moreno said.
If the president were forced to submit to an interview with Mueller's investigators, it would mark a precedent in American politics. Only Bill Clinton has received a subpoena while president, and he ultimately submitted to a voluntary interview.
Trump's attorney Jay Sekulow confirmed that his team had submitted a response to Mueller but declined to discuss specifics. Earlier Wednesday, Giuliani appeared on Sekulow's radio show and called for Mueller to end his probe before September, and said that his counter-proposal to Mueller was made in good faith.
"We do not want to run into the November elections," Giuliani said.
The special counsel has been tight-lipped as negotiations have dragged on. In contrast, Trump's team has provided prolific and conflicting reports to the media, leading some experts to worry that only one side of the story is being made public.
The special counsel declined a request for comment from CNBC.
— CNBC's Eamon Javers contributed to this report.