US president Donald Trump has used tweets to take out his frustrations over the intensifying Russia investigation by lashing out at special counsel Robert Mueller, hinting at a shift away from cooperating with a probe he believes is biased against him.

Mr Trump used weekend tweets to name Mr Mueller for the first time, 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.

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

The president’s aggressive stance followed a call by his personal lawyer for Rod Rosenstein, who Mr Trump appointed as deputy attorney general and who now oversees Mr Mueller’s inquiry, to “bring an end” to that investigation.

Republicans on the House Intelligence Committee, which spent the past year conducting a parallel investigation, recently said they drafted a report concluding there was no collusion or coordination between Mr Trump’s presidential campaign and Russia, but committee Democrats vehemently disagreed.

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

“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!”

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

In a move likely adding to Trump’s growing frustration, 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?” Trump tweeted on Sunday.

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

Mr Trump’s attacks raised new concerns among members of Congress that he could be seeking to orchestrate Mr Mueller’s firing. Republican and Democratic lawmakers warned the president to not even think about it.

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

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

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

Aides and friends said 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, CEO of the conservative news website Newsmax and a long-time Trump friend.

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.

“A great day for Democracy,” Mr Trump tweeted afterwards.

He asserted without elaboration that Mr McCabe, whose firing he had publicly urged, knew “all about the lies and corruption going on at the highest levels of the FBI!”

It was later reported that 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 accuracy.

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

“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 would not 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. Mr Comey, who is releasing a book next month, tweeted after Mr 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 his assertion that he was unfairly maligned by a White House he says declared “war” on the FBI and Mr Mueller’s investigation.

Mr Sessions said he dismissed Mr McCabe on the recommendation of FBI disciplinary officials who said Mr McCabe was not 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.

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.

Also over the weekend, Mr Trump’s personal lawyer, John Dowd, cited the “brilliant and courageous example” by Sessions and the FBI’s Office of Professional Responsibility and said Mr Rosenstein should “bring an end” to the Russia investigation “manufactured” by Mr Comey.

In response, Rep Trey Gowdy, said: “If you have an innocent client, Mr. Dowd, act like it.”

Mr Dowd said he was not calling on Mr Rosenstein to fire the special counsel immediately and had not discussed with him the idea of dismissing Mr Mueller or ending the probe. Mr Dowd also said he was speaking for himself and not the president.

Mr Mueller is investigating whether Mr Trump’s actions, including Mr Comey’s ouster, constitute obstruction of justice.