Republican senators have warned President Donald Trump not to fire Special Counsel Robert Mueller and say 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 on Friday of the bureau’s former deputy director, Andrew McCabe, two days before he was eligible to retire with a full pension.

Republican Senator Jeff Flake, who has criticised Mr Trump harshly, said the president’s latest comments appeared to be aimed at the firing of Mr Mueller.

Senator Lindsey Graham, another Republican, said if Mr Trump were to dismiss Mr Mueller it would mark “the beginning of the end of his presidency”.

Lindsey Graham gave a stern warning Sunday to President Donald Trump against firing special counsel Robert Mueller. Photo: Getty

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 Mr 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,” Mr Flake told CNN’s State of the Union on Sunday.

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

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

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

On Sunday, he attacked former FBI director James Comey and Mr McCabe, top officials who were involved in the Russia probe and subsequently fired.

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. Can we call them Fake Memos?

— Donald J. Trump (@realDonaldTrump) March 18, 2018

The US intelligence community has concluded that Moscow conducted an influence campaign aimed at swaying the 2016 presidential election to Mr Trump over Democratic candidate Hillary Clinton. Mr Mueller is investigating the Russian meddling and any possible collusion with the Trump campaign.

On Saturday, Trump’s personal lawyer John Dowd urged the Justice Department official overseeing Mueller, Rod Rosenstein, to “bring an end to alleged Russia Collusion investigation manufactured by McCabe’s boss James Comey”.

Mr Graham, a co-author of legislation that would make it harder for a president to fire a special counsel, said it was very important that Mueller be allowed to proceed without interference and that many Republicans share this view.

“The only reason Mr Mueller could ever be dismissed is for cause. I see no cause when it comes to Mr Mueller,”Mr  Graham said on CNN.

Another Republican, Senator James Lankford, said he does not believe Mr Trump would fire Mr Mueller.

-Reuters