Some conservatives were still concerned that the bill was too costly and did not do enough to roll back federal health insurance mandates. Moderates and others, meanwhile, were grappling with worries of their states’ governors and fretted that the loss of benefits would be too much for their constituents to bear.

Mr. Ryan had earlier postponed the initial House vote that was scheduled for Thursday to coincide with the seventh anniversary of the Affordable Care Act’s signing. Mr. Trump confronted the possibility of a humiliating loss on the first significant legislative push of his presidency.

At a White House meeting with members of the hard-line Freedom Caucus earlier on Thursday, Mr. Trump had agreed to the conservatives’ demands to strip federal health insurance requirements for basic benefits such as maternity care, emergency services, mental health and wellness visits from the bill. But that was not enough to placate the faction, part of the reason that Thursday’s vote was placed on hold.

As House leaders struggled to negotiate with holdouts in the hopes of rescheduling the vote, Mr. Trump sent senior officials to the Capitol with a blunt message: He would agree to no additional changes, and Republicans must either support the bill or resign themselves to leaving President Barack Obama’s signature domestic achievement in place.