WASHINGTON — After two false starts on President Trump’s promise to repeal the Affordable Care Act, Trump administration officials ratcheted up pressure on the House on Monday to vote on a revised version of the Republican repeal bill this week, even as support may actually be eroding.

The president complicated his pitch with a jumble of statements that indicated he did not fully understand the content of the measure he was pushing. He insisted that the repeal bill would protect Americans with pre-existing medical conditions, as the Affordable Care Act does. But a host of medical groups and disease advocacy organizations said it would not.

“I want it to be good for sick people,” Mr. Trump said in an interview with Bloomberg News. “It’s not in its final form right now. It will be every bit as good on pre-existing conditions as Obamacare.”

Representative Billy Long, Republican of Missouri, said on Monday: “I have always stated that one of the few good things about Obamacare is that people with pre-existing conditions would be covered.” The Republicans’ latest version “strips away any guarantee that pre-existing conditions would be covered and affordable,” he said.