President Donald Trump alongside Senate Majority Leader Mitch McConnell, R-Ky., talks to the media about Robert Mueller's report upon arriving for the Senate Republican Policy luncheon in the Capitol on Tuesday, March 26, 2019.

Senate Majority Leader Mitch McConnell told President Donald Trump the Senate will not revisit health care reform before the 2020 elections, the Kentucky Republican said Tuesday.

McConnell said he spoke with the president Monday afternoon and told him the Senate will not do anything "comprehensive" regarding health care until Republicans gain full control of Congress. Trump reignited the fight over the Affordable Care Act, also known as Obamacare, when his administration put its weight behind a lawsuit challenging the law's constitutionality late last month.

McConnell, who spoke to reporters after the weekly Senate Republican lunch on Capitol Hill, has long vowed to overturn the law. The Senate came just short of doing so in 2017 following a battle within the party over how best to replace Obamacare. Both Republicans and Democrats think the GOP's repeal effort was a driving force behind Republicans losing 40 House seats in last year's midterms.

McConnell's comments came after Trump tweeted Monday night that Republicans "are developing a really great HealthCare Plan with far lower premiums (cost) & deductibles than ObamaCare." He claimed they will vote on it in 2021 after "Republicans hold the Senate & win back the House" in next year's elections.

Trump repeatedly criticized Obamacare, pledging throughout his presidential campaign to do away with the health care law put in place by his predecessor, President Barack Obama. In March, the Department of Justice went further than it had before in trying to scrap the Affordable Care Act, supporting a federal judge's ruling that Obamacare is unconstitutional.

An estimated 30 million people would lose their coverage if Obamacare is repealed without another plan in place. However, McConnell said he doesn't suspect the courts will strike down Obamacare "anytime soon."

"There's no point in pushing the panic button," he said. "The court system takes a long time to resolve these issues."

When asked if McConnell saw any difference between himself and the president on health care, the majority leader said, "Not any longer."

The senator added that Trump accepted the Senate would not focus on health care for now and "that he would be developing a plan that he would take to the American people during the 2020 campaign." Trump would suggest the proposal is what he would advocate "in a second term if there were a Republican Congress," McConnell said.

The GOP currently holds 197 seats in the House, meaning it would need 21 more to win a majority.

In a series of tweets Wednesday morning, Trump denied that he asked McConnell for a vote before the election, adding that health care "will be a great campaign issue."

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The White House did not immediately respond to CNBC's request for comment.

— CNBC's Christina Wilkie contributed to this report.