Sarah Silbiger/The New York Times

WASHINGTON — President Trump backed off plans to introduce a Republican replacement for the Affordable Care Act after Senator Mitch McConnell privately warned him that the Senate would not revisit health care in a comprehensive way before the November 2020 elections.

Reversing himself in the face of Republican consternation, Mr. Trump said his party would not produce a health care plan of its own, as he had promised, until after the elections, meaning he will only try to fulfill his first-term promise to repeal and replace his predecessor’s signature program if he wins a second term.

The president’s abrupt about-face, announced on Twitter on Monday night after talking with Mr. McConnell, all but ensured that health care will take a central place in next year’s campaign, elevating an issue Democrats consider one of their strengths. But it may take the legislative heat off Republicans exasperated by Mr. Trump’s unexpected push to devise a wholesale replacement for President Barack Obama’s health law in the coming months.

“I made it clear to him that we were not going to be doing that in the Senate,” Mr. McConnell, the majority leader from Kentucky, said on Tuesday. “He did say, as he later tweeted, that he accepted that and that he would be developing a plan that he would take to the American people during the 2020 campaign.”

The president’s last attempt to replace Mr. Obama’s health care program blew up in 2017 when his party controlled both houses of Congress. Democrats seized the House in last year’s midterm elections in part on a promise to defend the most popular parts of the Affordable Care Act, so when Mr. Trump revived the issue last week, it distressed Republicans who consider it a political liability.

Mr. Trump had surprised allies by ordering his administration to ask a federal court to invalidate the entire Affordable Care Act and then promised a Republican replacement. Democrats, consumer groups, doctors, hospitals and insurance companies have said that 20 million people could lose health coverage if courts accept the administration’s argument.

Mr. McConnell said he spoke with Mr. Trump on Monday afternoon to explain that the Senate would not return to the issue in a broad way before the next election. “I pointed out to him the Senate Republicans’ view on dealing with comprehensive health care reform with a Democratic House of Representatives,” Mr. McConnell said.

But if that warning was meant to quiet the president, it did not work. Hours later, Mr. Trump wrote on Twitter, “The Republicans are developing a really great HealthCare Plan with far lower premiums (cost) & deductibles than ObamaCare.”

“In other words it will be far less expensive & much more usable than ObamaCare,” he said in a string of three tweets posted Monday night. “Vote will be taken right after the Election when Republicans hold the Senate & win back the House.”

Democrats jumped at the opening.

“Last night the president tweeted that they will come up with their plan in 2021,” Senator Chuck Schumer of New York, the Democratic leader, said at a rally in front of the Supreme Court. “Translation: they have no health care plan. It’s the same old song they’ve been singing. They’re for repeal. They have no replace.”

Mr. Trump appeared to be gambling that he could turn the tables on an issue that has long favored Democrats by portraying them as increasingly extreme….