Special counsel Robert Mueller announced his resignation on Wednesday from the United States Justice Department so that he can "return to public life".

In his first public comments on the probe into ties between Russia and US President Donald Trump's campaign, Mueller said “it would be unfair” to potentially accuse someone of a crime when the person couldn't stand trial to defend himself. He added that he believed he was constitutionally barred from charging Trump with a crime but emphasised that his report did not exonerate the president. He added that charging the president was “not an option” his team could consider in the probe.

The comments at an extraordinary press conference were Mueller's first public statements since his appointment as special counsel two years ago.

“If we had had confidence that the president clearly did not commit a crime, we would have said so,” Mueller said. “We did not, however, make a determination as to whether the president did commit a crime.”

The statement came amid demands for Mueller to testify on Capitol Hill about his findings and tension with Attorney General William Barr.

Mueller's comments echoed the findings in his public report into meddling in the 2016 campaign. His probe did not find that the Trump campaign coordinated to sway the presidential election. But, despite Trump's repeated assertions to the contrary, it did not reach a conclusion on whether Trump had obstructed justice.

Mueller had said in his report that he did not think it would be fair to publicly accuse the president of a crime if he was not going to charge him. A Justice Department legal opinion says sitting presidents cannot be indicted, and Mueller made clear in his report that that opinion helped shape the investigation's outcome and decisions.

Mueller's statement was expected to be relatively brief, about eight minutes, and Barr was given a heads-up about what he would say, according to people who were not authorised to provide details on the record and spoke on condition of anonymity.

Mueller and Barr have been at odds over the attorney general's handling of the special counsel's report on Russia's interference in the 2016 election and the possibility that Republican candidate Donald Trump's campaign cooperated with the Russians' efforts to help him win.

Mueller has remained a Justice Department employee since submitting the report in March, though the Justice Department has not said what work he has been doing.

Barr has said he was surprised that Mueller did not reach a conclusion, and he decided with Deputy Attorney General Rod Rosenstein that the evidence did not support an obstruction of justice allegation.

Mueller, for his part, privately complained to Barr that a four-page letter the attorney general wrote summarising his main conclusions did not adequately capture the investigation's findings. Barr called Mueller's letter “snitty” in congressional testimony this month in which he defended his decision to reach a conclusion on obstruction in place of Mueller.

House Democrats want Mueller to testify publicly, though no date or arrangements have been set, and it's not clear that he will.

Barr is currently in Alaska for work and is scheduled to participate in a round table discussion with local leaders in Anchorage later in the day.

A senior White House official said “the White House was notified” on Tuesday night that Mueller might make a statement on Wednesday.