Republican leaders had planned a vote on the measure after Trump cut off negotiations with Republicans who had balked at the plan and issued an ultimatum to vote on Friday, win or lose.
It was unclear whether the bill might be rescheduled, although Trump told the Washington Post, "We just pulled it."
Amid a chaotic scramble for votes, House of Representatives Speaker Paul Ryan, who has championed the bill, met with Trump at the White House before the bill was pulled from the House floor after hours of debate.
Without the bill's passage in Congress, Democratic former President Barack Obama's signature domestic policy achievement, the 2010 Affordable Care Act - known as Obamacare - would remain in place despite seven years of Republican promises to dismantle it.
Repealing and replacing Obamacare was a top campaign promise by Trump in the 2016 presidential election, as well as by most Republican candidates, "from dog-catcher on up," as White House spokesman Sean Spicer put it during a briefing on Friday.