Todd Heisler/The New York Times

TAMPA, Fla. — Mitt Romney’s supporters passed new rules governing future primaries over the loud boos of Ron Paul supporters and other conservative activists who had objected to what they said was a power grab by the party’s establishment leaders.

The House speaker, John A. Boehner, called for a vote on the rules on Tuesday afternoon after Mr. Romney’s advisers said they had reached a compromise with activists on Monday night.

When Mr. Boehner called for the “ayes,” the crowd roared in the affirmative. But when he called for the “nays,” an even louder “no” echoed through the convention hall, led by supporters of Mr. Paul.

Mr. Boehner ignored them, pressing ahead by saying the rules would be adopted “without objection,” even as the crowd continued to roar its disapproval. Mr. Boehner announced that the rules were approved and quickly moved on to the adoption of the party’s platform.

The loudest protests on the floor came from the back of the Texas delegation, from delegates in Lone Star shirts and white cowboy hats, and from a group adjacent to them at the far end of the hall to the right of the podium.

Advisers to Mr. Romney had proposed rules that would make it harder for a candidate like Mr. Paul to amass delegates to mount a challenge to a more established candidate.

Under the compromise, delegates would be selected by the state and local level without interference or control by the party’s presidential candidate. That would allow competing voices inside the convention, both sides said.

But in a nod to the concerns of Mr. Romney’s campaign, delegates sent on behalf of a candidate would be required to vote to nominate that candidate on the first ballot. If they tried to vote for someone else, their vote would be recorded for the candidate to whom they were bound.

The anger over that move had lingered for the last several days.

Opponents of Mr. Romney’s efforts to change the rules had threatened to disrupt the proceedings and embarrass the party’s soon-to-be nominee. But Mr. Boehner moved quickly, leaving the protesters little opportunity to catch airtime.