WASHINGTON — A formal condemnation of anti-Semitism that is up for a vote in the House this week has touched off a furious debate between older House Democrats and their young liberal colleagues over whether Representative Ilhan Omar is being singled out for unfair treatment over her statements on Israel.

The resolution, likely to be voted on Thursday, grew out of Ms. Omar’s suggestion last week that pro-Israel activists were pushing “for allegiance to a foreign country” — a remark that infuriated leading Jewish members of the House, who say it played into the anti-Semitic trope of “dual loyalty.”

It comes just weeks after Ms. Omar apologized for tweeting that support for Israel was “all about the Benjamins baby,” a reference to hundred-dollar bills that critics said echoed a common anti-Semitic belief that Jewish money is controlling foreign policy.

But progressives in the House and their allies have rallied to the defense of Ms. Omar, a freshman Democrat from Minnesota and one of the first two Muslim women elected to Congress, who was hailed as a trailblazer. Speaker Nancy Pelosi told top Democrats on Tuesday evening that the resolution would also include language condemning anti-Muslim bias as well — a move advocated by the Congressional Progressive Caucus.