WASHINGTON — President Trump stepped up his attacks against Robert Mueller on Sunday even as some Republican allies cautioned the president against any move to fire the special counsel, who is carrying out a broad investigation arising from Russian interference in the U.S. presidential election.

Tensions over the Mueller probe gained intensity from the firing late Friday night of Andrew McCabe, the former deputy director of the FBI. Attorney General Jeff Sessions fired McCabe just hours before he would have qualified for the full government pension given to law enforcement officers.

Trump, who had targeted McCabe, publicly cheered his removal.

McCabe is expected to be a significant witness in the Mueller investigation. News reports said that he kept notes about his encounters with Trump as well as memos about his conversations with fired FBI director James Comey. Mueller’s investigators have asked questions of witnesses that suggest they are looking at whether Trump’s firing of Comey was part of an effort to obstruct justice.

According to Justice Department officials, internal FBI overseers recommended that McCabe be fired over a matter unrelated to the Mueller probe — his handling of information about the FBI’s investigation of allegations against Hillary Clinton.

But Sessions’ decision to dismiss him, and the speed with which that happened, quickly became a talking point for both critics and defenders of the president in the context of the Russia investigation.

The president, who spent a sunny Sunday at his golf property in Virginia, began the day with a series of caustic early-morning tweets aimed at McCabe, Comey and Mueller.

One expressed doubts concerning whether McCabe had indeed documented details about their conversations. Trump tweeted that McCabe “never took notes when he was with me” and added that the memos were probably written at a later date “to help his own agenda.”

“Can we call them Fake Memos?” the president asked rhetorically.

When dealing with a sensitive legal matter, law enforcement personnel often document encounters in as much detail as they can recall, immediately after the fact, in what are known as contemporaneous memos.

Another presidential tweet accused Comey of lying to congressional investigators months ago, and yet another suggested that the investigative team of Mueller, a lifelong Republican, was tainted by political partisanship.

Speculation that the president might be preparing to move against Mueller took on new energy Saturday, when one of his lawyers, John Dowd, suggested that that the McCabe affair should serve as a prelude to a forced end to the special counsel’s investigation.

That drew a blunt warning Sunday from Sen. Lindsey Graham, R-S.C., who has said consistently that any attempt by the White House to halt Mueller’s work would be disastrous for Trump.

“If he tried to do that, it would be the beginning of the end of his presidency,” said Graham. “We are a rule-of-law nation.”

Interviewed on CNN’s “State of the Union,” Graham said that Mueller could only be dismissed for cause.

“I see no cause,” the senator said. “I think he’s doing a good job.”

“There are many Republicans who share my view,” he pointedly added.

Another South Carolina Republican, Rep. Trey Gowdy, took aim at Dowd, who had expressed hope Saturday that the “brilliant and courageous example” set by the firing of McCabe would “bring an end to the alleged Russia Collusion investigation.”

Dowd’s comments made it appear that Trump had something to hide, Gowdy said on “Fox News Sunday.”

“The president’s attorney frankly does him a disservice when he says that, and when he frames the investigation that way,” said Gowdy, who chairs the House Oversight Committee and is not running for re-election.

“If you have an innocent client, Mr. Dowd, act like it.”

But Gowdy said if Trump did move against Mueller, “I’m not sure the House can do a lot.”

One of the few Republicans who has spoken out strongly against Trump’s behavior on a wider range of issues predicted that the president would see a groundswell of opposition to any attempt to end the special counsel’s investigation.

“I don’t know what the designs are on Mueller, but it seems to be building toward that,” Sen. Jeff Flake of Arizona said on “State of the Union.”

He said he would expect “considerable pushback in the next couple of days, urging the president not to go there.”

Sen. Marco Rubio, R-Fla., also on “Meet the Press,” expressed misgivings about the circumstances of McCabe’s firing, hours before his birthday would have made him eligible for the full pension.

“I don’t like the way it happened,” Rubio said. “He (McCabe) should have been allowed to finish through the weekend.”The issue of whether McCabe will be stripped of his retirement benefits was still unclear Sunday.

Trump appeared to demand months ago that the former deputy director be fired in time to prevent him from collecting a pension earned over two decades of FBI service.

Some experts on federal employment suggested, however, that any loss of retirement income could be prevented if a member of Congress hired McCabe, thus keeping him on the federal payroll for at least a few more days.

Several lawmakers quickly offered to do so, sometimes accompanying their overtures with sardonic commentary on Twitter.

One of them, Rep. Mark Pocan, D-Wis., tweeted, “Andrew call me. I could use a good two-day report on the biggest crime families in Washington, D.C.”

Another Twitter message came from Rep. Luis Gutierrez, saying it was important to “stand up to bullies.”

“If you need a federal job, call me on Monday,” the Illinois Democrat said in a tweet directed at McCabe. “I am serious.”

laura.king@latimes.com