WASHINGTON -- President Trump isn't considering firing the special counsel investigating Russian election interference, a top White House lawyer said, after a cascade of Trump tweets revived chatter that the deeply frustrated president may be preparing to can the veteran prosecutor.

In a first for Mr. 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. Mr. 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 favor.

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

Get Breaking News Delivered to Your Inbox

Likely contributing to Mr. Trump's sense of frustration, The New York Times reported last week that Mueller had subpoenaed the Trump Organization for Russia-related documents. Mr. 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.

Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added...does anyone think this is fair? And yet, there is NO COLLUSION! — Donald J. Trump (@realDonaldTrump) March 18, 2018

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 Mr. 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, Mr. 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.

Mr. 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 Mr. Trump's reputation. Comey's yet-to-be-published book, "A Higher Loyalty," topped Amazon.com's best-seller list Sunday.

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

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

"If he tried to do that, that would be the beginning of the end of his presidency," said Sen. Lindsey Graham, R-South Carolina, a Trump ally.

Sen. Dick Durbin, D-Illinois, called for the passage of bipartisan bills designed to protect Mueller that have stalled in Congress.

"This president is engaged in desperate and reckless conduct to intimidate his law enforcement agencies of this country and to try and stop the special counsel. That is unacceptable in a democracy," Durbin said.

Mr. Trump's personal lawyer John Dowd called for Rosenstein to "bring an end" to the Russia investigation Saturday, adding to the tension.

Rep. Trey Gowdy, R-South Carolina, who sits on the House Intelligence Committee, appeared on "Fox News Sunday" to address Mr. Trump personally.

"My advice to the president is the same thing I just told his lawyer: give Bob Mueller the time, the independence and the resources to do the very job. Keep in mind, Chris, he didn't volunteer for this," Gowdy said addressing host Chris Wallace. "Give him the time, the resources, the independence to do his job, and when you are innocent, if the allegation is collusion with the Russians and there is no evidence of that, and you're innocent of that, act like it."

House Speaker Paul Ryan, R-Wisconsin, issued a statement regarding Mr. Trump and his harsh words for Mueller to the New York Times.

"As the speaker has always said, Mr. Mueller and his team should be able to do their job," a spokeswoman for Ryan told the Times.

His Senate counterpart, Majority Leader Mitch McConnell, R-Kentucky, has yet to comment on the ordeal.

Sen. Angus King, I-Maine, said on the CBS News broadcast "Face the Nation" Sunday it would be a "huge mistake" and "a true constitutional crisis" for the president to fire Mueller, whom he described as being "as straight an arrow as there is in America."

Mr. Trump cannot directly fire Mueller, who can only be dismissed for cause. Any dismissal would have to be carried out by Rod Rosenstein, the Trump-appointed deputy attorney general who has publicly expressed support for Mueller.

Aides and friends say they understand Mr. Trump's frustration.

"When he says it's a political witch hunt, I think he's right," said Christopher Ruddy, CEO of the conservative news website Newsmax and a longtime Trump friend.

Marc Short, Mr. Trump's congressional liaison, said the frustration is "well-warranted" because "there has been no evidence whatsoever of collusion."

Mr. Trump may have felt emboldened after Attorney General Jeff Sessions fired former FBI deputy director Andrew McCabe on Friday, something Mr. Trump had clamored for out of a belief that McCabe was part of the entrenched, anti-Mr. Trump bureaucracy. "A great day for Democracy," Mr. Trump tweeted afterward. Mr. Trump asserted without elaboration that McCabe knew "all about the lies and corruption going on at the highest levels of the FBI!"

The Associated Press later reported that McCabe kept personal memos detailing interactions with Mr. Trump that have been provided to Mueller's office and are similar to notes compiled by Comey. Mr. Trump sought to cast doubt on their veracity, tweeting Sunday that he spent "very little time" with 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?" Mr. Trump tweeted. It wouldn't be unusual for a senior official to make notes soon after meeting with the president.

The contents of McCabe's memos are unknown, but they could help substantiate McCabe's assertion that he was unfairly maligned by a White House he says had declared "war" on the FBI and Mueller's investigation.

Sessions said he dismissed McCabe on the recommendation of FBI disciplinary officials who said McCabe had not been candid with a watchdog office investigation. An upcoming inspector general's report is expected to conclude that McCabe had authorized the release of information to the media and was not forthcoming with the watchdog office as it examined the bureau's handling of an investigation into Clinton's emails.

McCabe has vigorously disputed the allegations and said his credibility came under attack as "part of a larger effort not just to slander me personally" but also the FBI and law enforcement.

Mueller is investigating whether Mr. Trump's actions, including Comey's ouster, constitute obstruction of justice.

Graham spoke on CNN's "State of the Union." Durbin appeared on "Fox News Sunday" and Short was interviewed on CBS' "Face the Nation."