(CNN) —  

House Republican leader Kevin McCarthy of California said Friday that Republicans are frustrated that Democrats “watered down” a resolution that passed a day earlier condemning anti-Semitism as well as anti-Muslim discrimination and other forms of hate and intolerance.

Asked to explain why 23 House Republicans voted to oppose the measure, McCarthy, who voted for the resolution, said during a news conference that Democrats had “watered down this amendment. The frustration on the Republican side was more that you watered down the amendment. Yes, we are always stronger when we speak with one voice, but I think America is very clear on this: We oppose anti-Semitism.”

The resolution that passed was brought to the House floor in the wake of comments related to Israel by freshman Democratic Rep. Ilhan Omar of Minnesota that sparked criticism, including from a number of House Democrats.

Draft text of the resolution was originally written to focus specifically on condemning anti-Semitism, but Democrats later changed the language to make the measure into a much broader condemnation of hate and intolerance of all kinds.

That change followed intense internal debate among House Democrats, some of whom thought Omar was being unfairly targeted over her comments as a woman of color and a Muslim.

A number of the House Republicans who voted against the resolution argued that Democrats should have directly rebuked Omar and her comments, but failed to do so because the resolution did not mention her by name or focus solely on rejecting anti-Semitism.

In a statement explaining her vote against the resolution, Rep. Liz Cheney of Wyoming, a member of GOP leadership, argued that the measure was “a sham put forward by Democrats to avoid condemning one of their own and denouncing vile anti-Semitism.”

Cheney argued that Omar “deserves to be rebuked, by name, and removed from the House Foreign Affairs Committee so that there is no mistake about the values and priorities that the House stands for.”

There was some frustration among House GOP leadership, however, over the vote, multiple aides told CNN, with Cheney’s decision to split from McCarthy and minority Whip Steve Scalise of Louisiana, who both voted for the resolution.

The view, according to one of the aides, is that had all Republicans voted for the resolution, it would have stayed solely a Democratic issue. Instead, the focus had now also been drawn to the 23 GOP “no” votes.

Pressed over the fact that Cheney, a member of his leadership team, was among those 23 Republicans against the measure, McCarthy conceded that his party is “stronger when we all vote together,” but said that “everybody has their own voting card.”

GOP Rep. Patrick McHenry of North Carolina, who voted in favor of the resolution, told CNN, “We had some members say, well, this is a sham, and they voted no as a matter of protest. Not about the contents of the resolution, but about the … stupid way that the Democrats acted in constructing this resolution.”

McHenry added, “I looked at and read the resolution, there was nothing I disagreed with in the resolution, and I voted for it. So others came to a different conclusion based off of the means of assembling this resolution.”

There were some House Democrats who stated publicly that they wished the matter had been handled differently and that there had been a resolution that focused specifically on rejecting anti-Semitism.

Democratic Rep. Eliot Engel of New York, the chairman of the House Foreign Affairs Committee, of which Omar is a member, said in remarks on the House floor ahead of the vote that while he would vote for the resolution, he wished the matter had been dealt with differently.

“I’m going to vote yes on this measure today,” he said, “Obviously, all forms of hatred and bigotry are intolerable and we should go on the record in saying so.”

But, Engel added, “I wish we had had a separate resolution about anti-Semitism. I think we deserved it. I think it was wrong not to have it.”

House Speaker Nancy Pelosi of California defended the resolution Friday in the face of GOP criticism that it had been watered down.

“I don’t think it watered down the anti-Semitic language at all. I think it strengthened it,” she said at an event sponsored by the Economic Club of Washington, DC.

Omar, who has not shied away from criticizing the actions of the Israeli government, became embroiled in a backlash after saying at an event last week, “I want to talk about the political influence in this country that says it is OK for people to push for allegiance to a foreign country.” The remark drew condemnation from several influential House Democrats.

After the resolution passed Thursday, Omar released a joint statement with Democratic Reps. Rashida Tlaib of Michigan and Andre Carson of Indiana praising the measure’s passage. All three lawmakers are Muslim.

“Today is historic on many fronts,” they wrote. “It’s the first time we have voted on a resolution condemning Anti-Muslim bigotry in our nation’s history.”

The statement continued, “We are tremendously proud to be part of a body that has put forth a condemnation of all forms of bigotry including anti-Semitism, racism, and white supremacy. At a time when extremism is on the rise, we must explicitly denounce religious intolerance of all kinds and acknowledge the pain felt by all communities. Our nation is having a difficult conversation and we believe this is great progress.”

CNN’s Phil Mattingly, Ashley Killough and Sunlen Serfaty contributed to this report.