He also warned that if they indulged the effort to strip Ms. Greene of her assignments, Democrats could try to target other Republicans, according to three people familiar with his comments, who insisted on anonymity to divulge the private exchange.
But Ms. Greene faced a greater backlash in the Senate after Mr. McConnell’s criticism.
“She’s not going to be the face of the party,” Senator Rick Scott of Florida, the chairman of Senate Republicans’ campaign arm, said of Ms. Greene. Mr. Scott, who was governor in 2018 when a gunman killed 17 people at a high school in Parkland, Fla., said her effort to portray the shooting as faked was “disgusting.”
“It’s beyond reprehensible for any elected official, especially a member of Congress, to parrot violent QAnon rhetoric and promote deranged conspiracies,” Senator Thom Tillis, Republican of North Carolina, wrote on Twitter. “It’s not conservative, it’s insane.”
The divergent reactions from House and Senate Republicans illustrated the extraordinary turmoil in the party as it struggles to define itself without Mr. Trump in the White House.
For her part, Ms. Greene offered a modicum of contrition in a brief speech, according to two people familiar with the remarks, and received applause from some lawmakers. She apologized for espousing a number of conspiracy theories and emphasized that she no longer believed in them.
She also sidestepped the issue of a Facebook post she made in 2018, unearthed by Media Matters for America, suggesting that a devastating wildfire that ravaged California was started by “a laser” beamed from space and controlled by a prominent Jewish banking family with connections to powerful Democrats.
Ms. Cheney’s victory was all the more remarkable because she refused to apologize for her impeachment vote, even as several members of the ultraconservative Freedom Caucus accused her of “aiding the enemy” in voting to impeach Mr. Trump, the people said. Representative Jim Jordan of Ohio, one of the former president’s fiercest defenders, joined in and said he felt Ms. Cheney could not represent a conference that had overwhelmingly voted against impeachment, given her own vote.