President Donald Trump has lashed out at what he considers to be the impartiality of an ongoing investigation into potential collusion with a foreign state.

Trump used Twitter on Sunday to criticise the legal basis of the Russia investigation by Special Counsel Robert Mueller.

"Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added … does anyone think this is fair? And yet, there is NO COLLUSION!

Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added...does anyone think this is fair? And yet, there is NO COLLUSION! — Donald J. Trump (@realDonaldTrump) March 18, 2018

It was the first time Trump mentioned Mueller by name, which led a group of Republican senators to suggest the president might be contemplating firing the special counsel.

Senator Lindsey Graham - co-author of legislation that would complicate the firing of a special counsel by the president - said Mueller's dismissal would spell "the beginning of the end of his [Trump's] presidency".

Senator Jeff Flake said Congress cannot stay quiet if the president decides to move in that direction.

"I don't know what the designs are on Mueller, but it seems to be building toward that [dismissing Mueller], and I just hope it doesn't go there, because it can't. We can't in Congress accept that," said Flake.

Trump's personal lawyer, John Dowd, has called on the Justice Department official overlooking the Russia investigation, Deputy Attorney General Rod Rosenstein, to "bring an end" to the probe.

Some Republicans, however, are asking why the president's lawyer is expending so much energy on a case where the president is presumably innocent.

"I think the president’s attorney, frankly, does him a disservice when he says that and when he frames the investigation that way ... If you have an innocent client, Mr Dowd, act like it," Representative Trey Gowdy told reporters on Sunday.

Republican House Speaker Paul Ryan requested that Mueller and his team be "able to do their job".

Sunday's developments come just days after FBI Deputy Director Andrew McCabe was dismissed, citing a "lack of candor" with regard to authorising personnel to talk to the media.