“Vote no, just vote no, because the fact is a vote yes is to give leverage to the other side and surrender leverage on the floor of the House,” Ms. Pelosi told reporters on Thursday.

At a meeting of House Democrats before the vote, Representative Alexandria Ocasio-Cortez of New York implored moderates to vote against the Republican-led motions and, in an implicit threat, added that she would make it clear to liberal activists which members supported the Republican measures, according to officials in the room.

But some moderate freshmen, including Representative Xochitl Torres Small of New Mexico, stood up and explained how difficult the votes have been for them.

House Republicans have sought to weaponize the procedural motion, using politically fraught measures to test the new Democrats’ resolve. The measures rarely hold the force of law, but a no vote even on a procedural motion could show up in a 30-second attack ad next year. Republicans succeeded in attaching a resolution condemning anti-Semitism and the boycott-Israel movement to a bill designed to halt American aid to Saudi Arabia’s war in Yemen after even Democratic leaders gave up on opposing it.

“All they want to do is feed red meat to their base,” Representative Veronica Escobar, Democrat of Texas, said of House Republicans. “I’m hoping that colleagues of mine will see it that way and understand that these procedural motions — even the best-worded procedural motion — has not had the chance to go through the process” of committee consideration.

Amid concern that some Democrats will continue to break away on tough votes, some House leaders are weighing revising the rules to require Republicans to give them more notice on the content of procedural motions.

Representative Joe Cunningham, Democrat of South Carolina, who has voted for Republican-backed motions, played down their importance on Thursday.