US President Donald Trump has lashed out at Russia probe special counsel Robert Mueller, signalling a possible shift away from a strategy of cooperating with a probe he believes is biased against him.

Key points: Mr Trump's attacks raised new concerns among members of Congress that he may be trying to orchestrate Mr Mueller's firing

Mr Trump's attacks raised new concerns among members of Congress that he may be trying to orchestrate Mr Mueller's firing The president cannot directly fire Mr Mueller, who can only be dismissed for cause

The president cannot directly fire Mr Mueller, who can only be dismissed for cause Senator Dick Durbin called for the passage of bipartisan bills designed to protect Mr Mueller

In a series of weekend tweets naming Mr Mueller for the first time, Mr Trump criticised the investigation into Russian interference in the 2016 presidential election and raised fresh concerns about the objectivity and political leanings of the members of Mr Mueller's team.

"The Mueller probe should never have been started in that there was no collusion and there was no crime," Mr Trump tweeted.

"It was based on fraudulent activities and a Fake Dossier paid for by Crooked Hillary and the DNC, and improperly used in FISA COURT for surveillance of my campaign. WITCH HUNT!"

Mr Trump was referring to a dossier of anti-Trump research funded by the Democratic Party and Hillary Clinton's campaign.

The New York Times reported last week that Mr Mueller had subpoenaed the Trump Organisation and requested Russia-related documents.

Mr Trump had said Mr Mueller would cross a red line with such a step.

"Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans?" Mr Trump tweeted.

Some of Mr Mueller's investigators indeed have contributed to Democratic political candidates, but US Justice Department policy and federal service law bar discrimination in the hiring of career positions on the basis of political affiliation.

Mr Mueller is a Republican.

The President's aggressive stance followed statements on Saturday by his personal lawyer, who called on Deputy Attorney-General Rod Rosenstein, who now oversees Mr Mueller's inquiry, to "bring an end" to that investigation.

McCabe, Comey, also targeted

Mr Trump also challenged the honesty of Andrew McCabe, the newly fired FBI deputy director, and James Comey, the bureau's former director whom Mr Trump fired last year over the Russia probe.

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Mr Trump asserted without elaboration that Mr McCabe, whose firing he had publicly called for, knew "all about the lies and corruption going on at the highest levels of the FBI!"

Mr McCabe kept personal memos detailing interactions with Mr Trump that have been provided to Mr Mueller's office and are similar to notes compiled by Mr Comey.

Mr Trump sought to cast doubt on their veracity.

"Spent very little time with Andrew McCabe, but he never took notes when he was with me," Mr Trump tweeted.

"I don't believe he made memos except to help his own agenda, probably at a later date. Same with lying James Comey. Can we call them Fake Memos?"

It wouldn't be unusual for a senior official to make notes soon after meeting with the president.

Mr Trump also claimed Mr Comey lied under oath at a Senate hearing by saying he had never been an anonymous source.

Republicans on the House Intelligence Committee, which spent the past year conducting a parallel investigation, recently said they had drafted a report concluding no collusion or coordination between Mr Trump's presidential campaign and Russia.

Committee Democrats vehemently disagreed.

'That would be the beginning of the end of his presidency'

Sorry, this video has expired John Barron provides analysis as to why Andrew McCabe was sacked

Mr Trump's attacks raised new concerns among members of Congress that he could be seeking to orchestrate Mr Mueller's firing.

But White House lawyer Ty Cobb said it was not the case.

"In response to media speculation and related questions being posed to the administration, the White House yet again confirms that the President is not considering or discussing the firing of the Special Counsel, Robert Mueller," Mr Cobb said.

Republican and Democratic politicians warned Mr Trump to not even think about firing Mr Mueller.

"If he tried to do that, that would be the beginning of the end of his presidency," said Senator Lindsey Graham, a Trump ally.

Senator Dick Durbin called for the passage of bipartisan bills designed to protect Mr Mueller that have stalled in Congress.

"This president is engaged in desperate and reckless conduct to intimidate his law enforcement agencies of this country and to try and stop the special counsel. That is unacceptable in a democracy," Mr Durbin said.

Mr Trump cannot directly fire Mr Mueller, who can only be dismissed for cause.

Any dismissal of Mr Mueller would have to be carried out by Mr Rosenstein, who has publicly expressed his support for Mr Mueller.

Trump's frustration 'well-warranted'

Aides and friends say they understand Mr Trump's frustration with an investigation that hangs over his presidency.

"When he says it's a political witch hunt, I think he's right," said Christopher Ruddy, chief executive of the conservative news website Newsmax and a longtime friend of Mr Trump.

Marc Short, Mr Trump's congressional liaison, said the president's frustration is "well-warranted" because "there has been no evidence whatsoever of collusion."

Mr Trump may have felt emboldened after Attorney-General Jeff Sessions fired Mr McCabe on Friday, local time.

"A great day for Democracy," Mr Trump tweeted afterward.

Sorry, this video has expired Deputy FBI director sacked

'The American people will hear my story very soon'

Mr Comey, who is releasing a book next month, tweeted after McCabe's firing: "Mr. President, the American people will hear my story very soon. And they can judge for themselves who is honourable and who is not."

The contents of Mr McCabe's memos are unknown, but they could help substantiate Mr McCabe's assertion that he was unfairly maligned by a White House he says had declared "war" on the FBI and Mr Mueller's investigation.

Attorney-General Jeff Sessions says he fired Mr McCabe on the recommendation of FBI officials. ( AP: Carolyn Kaster, File )

Mr Sessions said he dismissed Mr McCabe on the recommendation of FBI disciplinary officials who said Mr McCabe had not been candid with a watchdog office investigation.

An upcoming inspector general's report is expected to conclude that Mr McCabe had authorised the release of information to the media and was not forthcoming with the watchdog office as it examined the bureau's handling of an investigation into Mrs Clinton's emails.

Mr McCabe has vigorously disputed the allegations and said his credibility had been attacked as "part of a larger effort not just to slander me personally" but also the FBI and law enforcement.

AP