WASHINGTON — After frenzied late-night negotiations, Speaker Paul D. Ryan defused a moderate Republican rebellion on Tuesday with a promise to hold high-stakes votes on immigration next week, thrusting the divisive issue onto center stage during a difficult election season for Republicans.

The move by Mr. Ryan, announced late Tuesday by his office, was something of a defeat for the rebellious immigration moderates, who fell two signatures short of the 218 needed to force the House to act this month on bipartisan measures aimed more directly at helping young immigrants brought to the country illegally as children.

Instead, the House is most likely to vote on one hard-line immigration measure backed by President Trump and conservatives — and another more moderate compromise bill that was still being drafted, according to people familiar with the talks.

Had the rebels secured just two more signatures for their “discharge petition,” they would have also gotten votes on the Dream Act, a stand-alone bill backed by Democrats that includes a path to citizenship for the young undocumented immigrants known as Dreamers, and another bipartisan measure that couples a path to citizenship for Dreamers with beefed-up border security.