Republican senators yesterday warned President Donald Trump not to fire Special Counsel Robert Mueller, and said the president must let federal investigators looking into Russian meddling in the US election do their jobs.

The Republican president has renewed his Twitter attacks on both the Federal Bureau of Investigation and Mueller's probe since the firing of the bureau's former deputy director, Andrew McCabe, on Friday, two days before he was eligible to retire with a full pension.

Republican Senator Jeff Flake, who has criticised Trump harshly, said the president's latest comments appeared to be aimed at the firing of Mueller. Senator Lindsey Graham, another Republican, said if Trump were to dismiss Mueller it would mark "the beginning of the end of his presidency."

AshLee Strong, a spokeswoman for Republican House Speaker Paul Ryan, said: "As the speaker has always said, Mr Mueller and his team should be able to do their job."

The comments underscored the risks for Trump if he goes too far to thwart the federal probe.

"I don't know what the designs are on Mueller, but it seems to be building toward that [firing him], and I just hope it doesn't go there, because it can't. We can't in Congress accept that," Flake told CNN's "State of the Union."

“So I would expect to see considerable pushback in the next couple of days urging the president not to go there."

In a series of tweets over the weekend, Trump accused the FBI leadership of lies, corruption and leaking information. He called the Russia probe a politically motivated witch hunt.