Republicans have been aggressive this year in challenging Democrats over support for Israel — and some key Jewish advocacy groups say they fear it is backfiring and sowing more division over U.S. relations with its closest Middle East ally.

One official at J Street, an advocacy group, said attempts by the GOP to paint Democratic Rep. Ilhan Omar as anti-Semitic became “reckless.” Others said they worry that attempts to score political points over Israel have grown unseemly.

“I’m very concerned about the sort of weaponization of the U.S.-Israel relationship and frankly, the weaponization of the charges of anti-Semitism,” Jacob Isaacson, chief policy and political affairs officer of the American Jewish Congress, told The Washington Times. “I would prefer if politicians stick to the facts … and avoid accusing their fellow politicians of heinous crimes.”

For Republicans, those sentiments are a worrying sign that their hopes of highlighting what they see as a troubling split inside the Democratic Party may not be the winning political issue they had hoped.

Both parties’ attempts to claim best friend status with Israel date back decades, but this year has been particularly pointed, with Democrats adding several freshman lawmakers to their ranks who have been fierce critics of the Jewish state.

Ms. Omar, Minnesota Democrat, has pushed the envelope the furthest, questioning the motives of the fealty both parties show.

“It’s all about the Benjamins,” she said in a now-infamous tweet, suggesting the American Israel Public Affairs Committee bribed lawmakers into supporting its interests.

She drew rebukes from members of both parties, but Republicans and President Trump said more was needed. They demanded Democratic leaders explicitly call out Ms. Omar by condemning her comments through a formal resolution on the House floor or by stripping her of her position on the Foreign Affairs Committee.

Logan Bayroff, the communication director for J Street, told The Times that the backlash aimed at Ms. Omar escalated to “reckless” accusations of anti-Semitism. He said that rhetoric was not only shamefully “politically motivated” but ultimately undermined efforts to pursue bipartisan pro-Israel policies.

The Republican Jewish Coalition defended the GOP, and Mr. Trump in particular, saying they were raising important issues. It’s Democratic leaders who are allowing the conversation to deteriorate, the coalition said.

“The Democrats are the ones that have moved off their position,” said Neil Strauss, national spokesman for the group. “The Republican is the party that isn’t different from 10 or 15 years ago.”

On Capitol Hill, GOP leaders pointed to their handling of Rep. Steve King, a Republican lawmaker accused of promoting white nationalist beliefs, as a model for handling off-script lawmakers. After questionable quotes appeared in The New York Times, Mr. King was stripped of his committee assignments by the Republican Caucus.

Ms. Omar and fellow freshman Democrats Reps. Rashida Tlaib and Alexandria Ocasio-Cortez have made comments that crossed lines concerning Israel, the Jewish advocacy groups agreed. But they differed on the level of seriousness.

“Are there people in the Democratic Party that made anti-Semitic statements? Yes. Are there in the Republican Party that made anti-Semitic statements? Absolutely, yes. That doesn’t make either party anti-Semitic,” said Mark Mellman, president and CEO of the Democratic Majority for Israel.

Michael Makovsky, president of the Jewish Institute for National Security of America, said the views of the freshmen Democratic women were “purely anti-Semitic.” But he said that doesn’t reflect on the rest of Democrats, particularly the party’s congressional leadership or presidential candidates such as Vice President Joseph R. Biden and Sen. Kamala D. Harris.

Still, he said pro-Israel Democrats need to push back forcefully on a growing anti-Israel faction in the party.

“I want the Democratic Party to reform itself, to be more like the Clinton Democratic Party — pro-Israel,” he said.

A vote last month to condemn the Boycott, Divestment, Sanctions movement that wants to punish Israel for its policies toward the Palestinians showed the extent of the division.

The anti-BDS resolution cleared the House 398-17. Of those “No” votes, 16 were Democrats. Four other Democrats ducked taking a position by voting “present.”

Mr. Strauss said that suggested Democrats were “fracturing” in their support for Israel.

Mr. Mellman countered that while part of the party doesn’t support Israel, it was small compared to the 209 Democrats who did back the anti-BDS resolution.

“It’s a very small number. We don’t say if someone wins an election 92-8, we don’t say, ‘Oh, well, there’s a lot of division in that district,’” he said.

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