White House lawyer Ty Cobb said on Sunday that President Donald Trump was not considering or discussing firing special counsel Robert Mueller – even after the president directly lashed out at Mueller's probe during the weekend.

The lawyer's assurance wasn't likely to assuage concerns that the president would act against the special counsel, however. On Monday, Trump continued his social-media onslaught against the Mueller probe by again calling it a "witch hunt."

TOTAL WITCH HUNT TWEET

The president's latest attack on Mueller's investigation into Russian meddling in the 2016 election came soon after he promoted, in a tweet, Fox News host Sean Hannity's upcoming appearance on "Fox and Friends," a favorite of Trump's. Hannity would go on to say: "The only person that colluded in that campaign, with the Russians, was Hillary Clinton."

Cobb's statement Sunday night came after hours after Trump tweeted criticism of Mueller's investigation. On Saturday, John Dowd, one of Trump's personal lawyers representing him in the Russia probe, called for a quick end to Mueller's investigation.

"I pray that Acting Attorney General Rosenstein will follow the brilliant and courageous example of the FBI Office of Professional Responsibility and Attorney General Jeff Sessions and bring an end to alleged Russia Collusion investigation manufactured by McCabe's boss James Comey based upon a fraudulent and corrupt Dossier," Dowd wrote in a statement provided to CNBC. The Daily Beast first reported it Saturday morning.

The president followed suit over the weekend with a series of tweets targeting Mueller's probe, fired FBI Director James Comey and the recently fired former FBI deputy director, Andrew McCabe.

SATURDAY TRUMP MUELLER TWEET

TRUMP MUELLER TWEET

Dowd's statement and Trump's subsequent tweets set off renewed speculation that the president might fire the special council. Even some Republicans voiced their concern over the matter.

Firing Mueller "would be the beginning of the end of his presidency," said Sen. Lindsey Graham of South Carolina. Republican Sen. John McCain, a frequent Trump critic, tweeted that Mueller should be able to complete his investigation "unimpeded."

McCain tweet

Sunday night, however, Cobb, another of the president's attorneys, sought to tamp down speculation that Trump would move soon to fire Mueller.

"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," Cobb said.

Reuters, The Associated Press and CNBC's Valerie Block and Javier David contributed to this report.