Senate Minority Leader Sen. Chuck Schumer of N.Y., center, speaks to reporters following the weekly Democratic policy luncheon on Capitol Hill in Washington, Tuesday, Oct. 31, 2017. (AP Photo/Susan Walsh)

Senate Minority Leader Sen. Chuck Schumer of N.Y., center, speaks to reporters following the weekly Democratic policy luncheon on Capitol Hill in Washington, Tuesday, Oct. 31, 2017. (AP Photo/Susan Walsh)

WASHINGTON (AP) — Senate Majority Leader Mitch McConnell exhibited no interest Tuesday in considering legislation shielding the special counsel from Donald Trump, even as Republicans warn the president against interfering with Robert Mueller’s investigation.

McConnell’s remarks came as Trump has continued using Twitter to complain about the continued focus on “phony Trump/Russia” connections, instead of on Hillary Clinton and Democrats. They also came a day after Mueller’s inquiry into Russian meddling during the 2016 presidential race yielded a guilty plea and two indictments of Trump campaign officials.

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Two bipartisan bills were introduced months ago that would make it harder for a special counsel to be fired. After an initial flurry of support, the bills have stalled as Trump has softened his public criticism of Mueller.

“We’ve got plenty of things we have to do between now and the end of the year that will take up floor time,” McConnell, R-Ky., said Tuesday when asked if he’d bring the measures to the Senate floor if Trump impedes Mueller’s work.

At one point, Trump’s legal team looked into potential conflicts surrounding the team Mueller has hired, including the backgrounds of members and political contributions by some members of his team to Clinton.

McConnell, who has expressed confidence in Mueller’s work, said the Senate’s role in the investigation is being performed by the chamber’s Intelligence committee.

“That’s our role in it, and special counsel has his job to do, and we’re going to concentrate on what we’re doing here,” said McConnell.

Senate Minority Leader Chuck Schumer, D-N.Y., said in a brief interview that he’d not asked McConnell to bring the bills protecting Mueller to the Senate floor, saying, “We’ll see what happens.” On Monday, Schumer called for swift congressional action should Trump interfere with the investigation.

Legislation sponsored by Sen. Lindsey Graham, R-S.C., would prevent the firing of any special counsel unless the dismissal was first reviewed by a panel of three federal judges. Legislation co-sponsored by Sen. Thom Tillis, R-N.C., would let any Justice Department special counsel challenge their removal in court.

The Senate GOP’s No. 2 leader complimented the guilty plea by George Papadopoulos for lying to FBI agents about Russian contacts.

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“I think hopefully it will send a message to everybody else to cooperate with the investigation and to answer the FBI’s questions and not to lie,” said Sen. John Cornyn, R-Texas. “So I thought that was a very positive move from that standpoint.”

Other Republicans made clear their opposition to any presidential interference in Mueller’s work, including Sen. Roy Blunt, R-Mo., another GOP leader. Blunt said he wasn’t concerned that Trump might take on Mueller more aggressively but added, “I’m also not for it.” He said firing Mueller “would be a big mistake.”

“Everybody that I know does not think that’s a good idea,” Sen. John McCain, R-Ariz., who’s clashed with Trump, said of a Mueller firing. “I don’t know what the actual reaction would be if it happened. I doubt if it’s going to, but I’ve been wrong almost every time.”

Jay Sekulow, Trump’s personal lawyer, shot down the possibilities of firing Mueller and or the president pardoning people caught up in the probe.

“The president has not indicated to me or to anyone else that I work with that he has any intent on terminating Robert Mueller,” Sekulow said in an interview Tuesday with ABC’s “Good Morning America.”

On pardons, he said: “I have not had a conversation with the president regarding pardons. And pardons are not on the table.”

Besides Papadopoulos’ guilty plea, former Trump campaign chairman Paul Manafort and his associate Rick Gates have both pleaded not guilty to conspiracy and money laundering charges.

White House spokeswoman Sarah Huckabee Sanders told reporters after the charges were released that “there is no intention or plan to make any changes in regards to the special counsel.”

Lawmakers have been on guard since May, when Trump abruptly fired FBI Director James Comey and Mueller was appointed.

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AP reporter Matthew Daly contributed.