Representative Ayanna Pressley, Democrat of Massachusetts, said she told leadership that there must be “equity in our outrage,” noting that Ms. Omar, a Minnesotan and one of the first two Muslim women elected to Congress, was being attacked for her faith.

“Islamophobia needs to be included” in the anti-Semitism resolution, she told reporters on Wednesday. “We need to denounce all forms of hate. There is no hierarchy of hurt.”

The closed-door meeting, the weekly gathering of House Democrats at the Capitol, generally involves discussion of the legislative agenda and political strategy. Instead, according to multiple people present, it turned into a gripe session over the treatment of Ms. Omar by her own party.

“What would be the appropriate level of punishment — a public flogging?” Representative Raúl Grijalva of Arizona, the chairman of the House Natural Resources Committee, asked in an interview after the meeting.

“We are all responsible for what we say, and there are consequences, whether it is this resolution or something else,” Mr. Grijalva said. “But there is a double standard we have to be aware of. The level of condemnation on Ms. Omar has been really intense.”

The resolution began as a response to Ms. Omar’s suggestion last week that pro-Israel activists were pushing “for allegiance to a foreign country,” a remark that her critics say played into the anti-Semitic trope of “dual loyalty.”

Representatives Eliot L. Engel and Nita M. Lowey — both New Yorkers who lead powerful committees — and other Jewish lawmakers discussed the comment over the weekend, bringing in Ms. Pelosi and Mr. Hoyer; by Tuesday, a resolution condemning anti-Semitism was circulating on Capitol Hill, surprising lawmakers who had not heard about it.