The decision came after Trump, who ran as a master dealmaker, failed to reach agreement with a bloc of rebellious conservatives.
Moderate-leaning Republican lawmakers were also bailing on the legislation, leaving it short of votes.
The bill could still come to a vote in coming days, but canceling today's vote was a significant defeat. It came on the seven-year anniversary of President Barack Obama signing the Affordable Care Act, years that Republicans have devoted to promising repeal.
"No deal," House Freedom Caucus Chairman Mark Meadows, R-N.C., said after he and his group of more than two dozen rebellious conservatives met with Trump to try to get more concessions to reduce requirements on insurance companies.
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The Republican legislation would halt Obama's tax penalties against people who don't buy coverage and cut the federal-state Medicaid program for low earners, which the Obama statute had expanded.
It would provide tax credits to help people pay medical bills, though generally skimpier than Obama's statute provides. It also would allow insurers to charge older Americans more and repeal tax boosts the law imposed on high-income people and health industry companies.
In a danger sign for Republicans, a Quinnipiac University poll found that people disapprove of the GOP legislation by 56 percent to 17 percent, with 26 percent undecided. Trump's handling of health care was viewed unfavorably by 6 in 10.
The survey was conducted March 16 to 21 with a margin of sampling error of plus or minus 3 percentage points. GOP leaders had targeted today for the climactic vote, in part because it marks the seventh anniversary of Obama's signing the measure into law.
House Minority Leader Nancy Pelosi, D-Calif., couldn't resist a dig.
"You may be a great negotiator," she said of Trump. "Rookie's error for bringing this up on a day when clearly you're not ready.