The number of Americans without health insurance would grow by 24 million under a House Republican proposal to topple most of the Affordable Care Act, according to a nonpartisan report that is likely to complicate GOP lawmakers’ efforts to unite around the plan.

The report, released Monday by the Congressional Budget Office, rattled some centrist Republicans in the Senate who have said they won’t support legislation that leaves a large number of people without coverage. House Republicans hoping to push the legislation through...