The question of whether U.S. President Donald Trump will fire special counsel Robert Mueller presumably put to rest again as of Monday - if not directly by Trump himself, then by White House attorney Ty Cobb.

Cobb issuing a statement Sunday night after at least two prominent Republican Senators issued sharp rebukes to Trump's weekend Twitter attacks against both the FBI and Mueller's federal probe into Russian meddling in the 2016 presidential election.

Cobb said: "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."

The statement came after Senator Lindsey Graham on CNN Sunday said that if Trump were to dismiss Mueller it would be "the end of his presidency".

Fellow Republican Jeff Flake, a frequent Trump critic, told CNN he hopes Trump "doesn't go there", adding, "We can't in Congress accept that".

Trump has increasingly attacked the special counsel's investigation, on Sunday first going after former FBI director James Comey, then just-fired former FBI Deputy Director Andrew McCabe… and finally tweeting, 'Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans?'

Mueller is a long-time registered Republican. He dismissed members of his team in the past for sending private messages that could suggest anti-Trump bias.

Despite Cobb's statement Sunday night, Trump again lashed out about the investigation on Monday, tweeting, 'It's a total witchhunt with massive conflicts of interest.'