In a first for Trump, he jabbed directly at special counsel Robert Mueller by name in weekend tweets that both challenged the investigation's existence and suggested political bias on the part of Mueller's investigators.

Trump has long been frustrated by the lengthy and intensifying probe, and insists his 2016 presidential campaign did not collude with Russia to influence the election in his favour.

"The Mueller probe should never have been started in that there was no collusion and there was no crime," he said in a Saturday tweet he ended with "WITCH HUNT!"

Likely contributing to Trump's sense of frustration, The New York Times reported last week that Mueller had subpoenaed the Trump Organisation for Russia-related documents. Trump had said 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?" he tweeted Sunday.

Some of Mueller's investigators indeed 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. Mueller is a Republican.

The tweets revived talk that Trump may, in an attempt to end the investigation, move to have Mueller fired. But White House lawyer Ty Cobb sought late Sunday to tamp down the speculation by saying the president is not contemplating such a move.

"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."

Deeply frustrated, Trump has fumed to confidants that the Mueller probe is "going to choke the life out of" his presidency if allowed to continue unabated indefinitely, according to an outside adviser who insisted on anonymity to discuss private conversations with the president.

Trump has long believed that the entrenched bureaucracy, particularly at the Justice Department and FBI, is out to thwart him. He fumed to one confidant after seeing a promotion for a forthcoming book by James Comey, the FBI director he fired last year, believing Comey will seek to enrich himself by besmirching Trump's reputation. Comey's book, A Higher Loyalty, topped Amazon.com's best-seller list on Sunday.

The president also has long been torn over how to approach the probe. His legal team, namely Cobb, has counseled Trump to cooperate with Mueller. But some former campaign advisers have urged Trump to be combative, warning that the investigation poses an existential threat to his presidency.

Members of Congress warned Trump to not even think about terminating Mueller.

Australian Associated Press