US President Donald Trump on Sunday attacked special counsel Robert Mueller's investigation into Russia's election meddling as unfair, insisting the probe is staffed with "hardened" Democrats.

"Does anyone think this is fair? And yet, there is NO COLLUSION!" Trump tweeted.

The salvo was the latest in an intensifying confrontation over Mueller's probe into whether Trump's campaign colluded with Russian attempts to sway the 2016 election in his favour.

The president also took aim at former FBI deputy director Andrew McCabe, who was fired on Friday, two days before he was due to retire, and former FBI director James Comey, who Trump sacked last year over the Russia probe.

Until now, the president has steered clear of directly attacking Mueller, the former FBI director who took over the Russia probe after Comey's firing on May 9, 2017.

"Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added," Trump said.

Widely respected in both political camps, Mueller was appointed FBI chief by the Republican president George W Bush, and kept on under the Democrat Barack Obama.

Lawmakers have repeatedly warned that any attempt by the president to oust him as special counsel would cross a red line.

In earlier tweets, Trump accused Comey of lying under oath in congressional testimony and dismissed as "fake memos" contemporaneous notes McCabe and Comey took of their interactions with the president.

Those memos could be fodder for Mueller's probe if he is pursuing potential obstruction of justice by the president.

"Spent very little time with Andrew McCabe, but he never took notes when he was with me. I don't believe he made memos except to help his own agenda, probably at a later date. Same with lying James Comey."

After his firing, McCabe said he was the victim of a Trump administration "war" against the FBI and the special counsel.

Comey has pushed back as well. "Mr President, the American people will hear my story very soon. And they can judge for themselves who is honourable and who is not," he tweeted on Saturday.