In a statement on Saturday, Mr. Schumer said: “The president wanted to make another run at repeal and replace, and I told the president that’s off the table. If he wants to work together to improve the existing health care system, we Democrats are open to his suggestions. A good place to start might be the Alexander-Murray negotiations that would stabilize the system and lower costs.”
Senators Lamar Alexander, Republican of Tennessee, and Patty Murray, Democrat of Washington, have held on-again, off-again talks about a bipartisan plan to stabilize the insurance markets under the Affordable Care Act, which have been roiled, in part, by the persistent uncertainty over the fate of the law.
Their negotiations were revived after the latest Republican repeal-and-replace bill, sponsored by Senators Lindsey Graham of South Carolina and Bill Cassidy of Louisiana, collapsed because of a lack of votes.
An aide to Mr. Schumer said the timing of Mr. Trump’s call was particularly awkward, given that the administration had just announced rules to expand the right of employers to deny women coverage for contraception on religious grounds — a move widely condemned by Democrats.
The Trump administration, the aide said, needed to stop sabotaging the law before bipartisan negotiations could begin.
Mr. Trump has established an easy rapport with “Chuck and Nancy,” as he likes to call Mr. Schumer, a fellow New Yorker, and Ms. Pelosi, of California. The three bonded last month over a dinner of honey sesame crispy beef in the White House, and their discussions have gone beyond the fiscal deal and how to protect young immigrants brought to this country illegally from being deported.
They have prodded Mr. Trump to put aside the Republican credo of “repeal and replace” in favor of more modest tweaks to the existing law. They have urged him to preserve subsidies, known as cost-sharing reductions, paid to insurers under the health law to help low-income consumers pay for out-of-pocket health expenses like co-payments and deductibles.
But Mr. Schumer’s quick rebuff of Mr. Trump on Friday shows the limits of the partnership. The senator has said that much will depend on whether the president keeps his promise to protect the young undocumented immigrants who are beneficiaries of the program known as Deferred Action for Childhood Arrivals, or DACA.
“Whether he pivots or not will be one of the most fundamental questions of this administration,” Mr. Schumer said recently. “It’s the $64,000 question. The only way it can happen is if we have a successful negotiation on DACA, and secondly whether we get health care.”
The president’s call is sure to further rankle Republicans, with whom Mr. Trump has had increasingly tense relations over their failure to knock down a key pillar of Mr. Obama’s legacy.
Mr. Trump’s latest move comes at a sensitive moment. The White House is working with Republicans on an ambitious plan to rewrite the tax code, perhaps the party’s last chance for a major legislative victory this year.
The president is also widely expected to decline to recertify the Iran nuclear agreement, a decision that would kick the matter to Congress, which would have to decide whether to reimpose sanctions on Iran and potentially blow up the deal negotiated by the Obama administration.
Mr. Trump’s tweet about his call to Mr. Schumer came during another busy weekend morning on social media for him. He railed against late-night talk show hosts and NBC News for what he said was their persistently negative and inaccurate coverage of him.
But he also praised The Washington Post — a frequent target of his “fake news” rants — for an article about how Mr. Trump’s fund-raising appeals to his political base have swelled the coffers of the Republican Party.
And in what has become an almost weekly ritual, Mr. Trump promised residents of Louisiana, Mississippi, Alabama and Florida that the federal government was mustering resources to deal with the next approaching hurricane, Nate. “Please listen to your local authorities & be safe!” he wrote.
For Mr. Trump, it was a relatively rare weekend in Washington. On Saturday evening, however, he was scheduled to fly to Greensboro, N.C., to attend a roundtable discussion and dinner with Republican donors.