(Adds Omar statement)

By Amanda Becker

WASHINGTON, March 7 (Reuters) - The U.S. House of Representatives approved a broad resolution condemning bigotry on Thursday after remarks by a Democratic member that some viewed as anti-Semitic exposed an ideological and generational rift in the party.

Some Democrats, including several U.S. senators who are seeking the party's 2020 presidential nomination, warned that party leaders were playing into Republicans' hands and had stymied legitimate debate over U.S.-Israel policy.

The House, which is controlled by Democrats, approved the resolution condemning anti-Semitism, anti-Muslim discrimination and other forms of bigotry by a 407-to-23 vote.

The vote came less than a week after Representative Ilhan Omar, one of the two first Muslim women elected to Congress, made statements at a Washington event that were denounced by some as anti-Semitic.

The resolution does not mention Omar by name. But Republicans have seized on Omar's statements and the resulting intra-party conflict as a sign the Democratic Party is fractured.

Many Democrats, in turn, have said House leaders were cowed by a Republican effort to divert attention from bigotry within their own ranks and that Omar is being held to a different standard.

"Unfortunately, I think the Democratic leadership here has made what I think is a pretty serious mistake in caving to this pressure," said Democratic strategist Peter Daou, who has advised Hillary Clinton and John Kerry.

The disagreement began after Omar, in an appearance at a Washington book store, said she feared that statements she and fellow Representative Rashida Tlaib made about foreign policy and the pro-Israel lobbying group the American Israel Public Affairs Committee (AIPAC) would be viewed as anti-Semitic because they are Muslim.

"I want to talk about the political influence in this country that says it's OK for people to push for allegiance to a foreign country. I want to ask why is it OK for me to talk about the influence of the NRA (National Rifle Association), of fossil fuel industries or Big Pharma, and not talk about a powerful lobbying group that is influencing policies?" Omar said.

Omar's critics denounced the statement as playing into the anti-Semitic trope that Jewish Americans are loyal to Israel over the United States. Omar said opposing the policies of Israel and Prime Minister Benjamin Netanyahu is not synonymous with anti-Semitism.

Omar, in a joint statement issued after Thursday's vote with Tlaib and Representative Andre Carson, a Democrat from Indiana, said "we are tremendously proud to be part of a body that has put forth a condemnation of all forms of bigotry."

Omar had previously apologized for February tweets that her critics said suggested Jewish Americans used money to influence pro-Israel U.S. policies.

Representative Liz Cheney, the No. 3 House Republican, told reporters on Wednesday that Omar "embodies a vile, hate-filled, anti-Semitic, anti-Israel bigotry."

President Donald Trump on Twitter on Wednesday called the Democratic response "shameful."

Cheney, complaining that the House should have "rebuked" Omar by name and removed her from the Foreign Affairs Committee, voted against the resolution.

Other Republicans who voted no, such as Chris Collins of New York, said the bill was not "strong enough in support of Israel, the only true democracy in the Middle East."

Republican Representative Steve King, who was condemned by the House in January for questioning why white supremacy is considered offensive, voted present.

Democrats had been divided over how best to handle Omar's comments.

Democratic Representative Eliot Engel, who chairs the Foreign Affairs Committee, said he welcomes policy debate but that it was "deeply offensive to call into question the loyalty of fellow American citizens because of their political views, including the U.S.-Israel relationship."

Young, progressive House newcomers like Representative Alexandria Ocasio-Cortez and several Democratic presidential candidates, however, came to Omar's defense.

Senator Bernie Sanders said in a statement that "we must not ... equate anti-Semitism with legitimate criticism of the right-wing, Netanyahu government." Senator Elizabeth Warren said "branding criticism of Israel as automatically anti-Semitic has a chilling effect on our public discourse." Senator Kamala Harris said she was concerned about Omar's safety.

Daou, the Democratic strategist, said a political double standard was at play, pointing to a recent tweet from Republican Representative Jim Jordan that used a dollar sign for a letter in the name of Democratic donor Tom Steyer, who is Jewish.

"Why is it that a white, male Republican can largely get away with the same thing and this massive outcry happened over a Muslim, progressive woman of color? That's something we have to grapple with," Daou said.

(Reporting by Amanda Becker Additional reporting by Richard Cowan Editing by Tom Brown, Leslie Adler and Lisa Shumaker)

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