House Speaker Nancy Pelosi, in a statement following House Republicans' removal of Cheney as GOP conference chair by a voice vote, called out to "reasonable Republicans across the country" to "take back their party."

"Congresswoman Liz Cheney is a leader of great courage, patriotism and integrity. Today, House Republicans declared that those values are unwelcome in the Republican party," she said. "The Republican denial of the truth presented by Congresswoman Cheney is reflected in their denial of the need to seek the truth in a January 6th commission and to repair the damage of January 6th with a security supplemental immediately."

House Minority Leader Kevin McCarthy did not speak after the vote concluded behind closed doors.

Senate Minority Leader Mitch McConnell, asked by reporters for his reaction to Cheney's ouster and what it means for the future of the GOP, did not answer.

He made no mention of the then just-completed House Republican conference vote to boot Cheney from leadership in his Senate floor speech Wednesday morning, either.

While McConnell publicly defended Cheney in February, when she first faced a challenge in the wake of voting to impeach the former president, he has stayed silent on her fate this time around.

-ABC News' Trish Turner

Sen. Dick Durbin, D-Ill., following the vote to remove Cheney from her leadership posted told Capitol Hill reporters it's a "sad day for the American Republican Party."

"It was an act of pure cowardice for them to remove her from leadership, and then to do it by a secret voice vote. That just tells the whole story as far as I am concerned," he said. "Donald Trump owns the soul of the Republican Party of America, and it was proved today in the House Representatives."

Senate Majority Leader Chuck Schumer said the House GOP has reached "a new and very dangerous low point" in ousting the Wyoming representative from leadership.

Republican Sen. Mitt Romney of Utah, another enemy of the former president like Cheney, on Tuesday warned in a tweet, "Expelling Liz Cheney from leadership won’t gain the GOP one additional voter, but it will cost us quite a few."

After the GOP Conference meeting, Cheney spoke to reporters and repeated that she is committed to advancing the Republican Party -- but not the agenda of the former president.

"I am absolutely committed as I said last night, as I said just now to my colleagues, that we must go forward based on truth. We cannot both embrace the big lie and embrace the Constitution," she said. "The nation needs a strong Republican Party, the nation needs a party that that is based upon fundamental principles of conservatism, and I am committed and dedicated to ensuring that that's how this party goes forward, and I plan to lead the fight to do that."

Asked if she was concerned that Trump might end up back in the Oval Office, Cheney said she "will do everything I can to ensure that the former president never again gets anywhere near the Oval Office."

"We have seen the danger that he continues to provoke with his language. We have seen his lack of commitment and dedication to the Constitution. And I think it's very important that we make sure whomever we elect, is somebody who will be faithful to the Constitution," she said.

She said she didn't feel betrayed by her colleagues' vote, when asked, but warned of the GOP falling in line with the former president's "very dangerous lies" and said there's work to do for the future of the party.

"I do not. I think that it is an indication of where the Republican Party is, and I think that the party is in a place that we've got to bring it back from, And we've got to get back to a position where we are a party that can fight for conservative principles that can fight for substance, we cannot be dragged backward, by the very dangerous lies of a former president," she said.

Former President Donald Trump, in a series of statements Wednesday as the vote was happening, attacked Cheney with personal insults -- following through on his promise since leaving office to inflict revenge on his enemies.

"Liz Cheney is a bitter, horrible human being," Trump said in a statement following her ouster. "She is a warmonger whose family stupidly pushed us into the never-ending Middle East Disaster, draining our wealth and depleting our Great Military, the worst decision in our Country’s history. I look forward to soon watching her as a Paid Contributor on CNN or MSDNC!'"

In an earlier statement ahead of the vote, Trump encouraged her removal and said Cheney has "absolutely no personality or heart."

Despite Trump's attacks, Cheney is not backing down from her criticisms, vowing after the vote to "do everything I can to ensure the former president never gets anywhere near the Oval Office."