Donald Trump's legal team has told special counsel Robert Mueller the US president will not answer any more questions in the probe of Russia's meddling in the 2016 election.

Trump submitted written answers to questions from Mueller in late November.

Trump lawyer Rudy Giuliani said Mueller raised the possibility of follow-up questions but that the president's outside legal team told the special counsel before Christmas that Trump would not respond.

Trump's lawyers and Mueller's team have had no contact since then, Giuliani said.

"As far as we're concerned, everything is over," Giuliani told Reuters.

"We weren't convinced they had any questions they don't know the answer to."

"They could try to subpoena him if they want. But they know we could fight that like hell," he said.

Peter Carr, a spokesman for Mueller, declined to comment.

US intelligence agencies have concluded that Russia interfered in the 2016 presidential election to try to tip it toward Trump by undermining Democratic candidate Hillary Clinton.

Trump has denied any collusion with Moscow and Russia has said it did not meddle in the election.

It is not clear when the special counsel will wrap up his probe. Mueller has been investigating Russian interference in the election and possible collusion with the Trump campaign since he was appointed in May 2017. The term of the Washington DC, grand jury Mueller is using was recently extended.

The president's lawyer said it was time for the special counsel to issue his report.

"Put up or shut up," Giuliani said. "We challenge you to do it."

Mueller is expected to send a confidential report on his findings to the Justice Department at the conclusion of his work. The report could ultimately be made public.