Instead, Mr. Trump said in the statement that lawmakers should support immigration legislation drafted by Senator Charles E. Grassley, Republican of Iowa, to codify his own plan. The bill would provide a path to citizenship for 1.8 million young immigrants, end the visa lottery program, build a border wall and end what he calls “chain migration,” which is family-based immigration.
“The overwhelming majority of American voters support a plan that fulfills the Framework’s four pillars, which move us towards the safe, modern, and lawful immigration system our people deserve,” Mr. Trump said.
He added that he would oppose a smaller, “Band-aid” approach to immigration that some lawmakers have been discussing, which would protect Dreamers for a few years in exchange for a small increase in border security spending — essentially kicking the issue down the road.
Senator Chuck Schumer of New York, the Democratic leader, responded harshly to the president’s entreaty.
“The American people know what’s going on,” Mr. Schumer said on the Senate floor. “They know this president not only created the problem, but seems to be against every solution that might pass because it isn’t 100 percent of what he wants. If, at the end of the week, we are unable to find a bill that can pass — and I sincerely hope that’s not the case due to the good efforts of so many people on both sides of the aisle — the responsibility will fall entirely on the president’s shoulders and those in this body who went along with him.”
Mr. Trump’s statement was a victory for conservatives in his administration, including Stephen Miller, his top domestic policy adviser, who have been pushing the president to demand an overhaul of the nation’s immigration rules in exchange for his support of a permanent solution for the Dreamers.
The top Republicans in both the House and Senate praised the president’s statement, describing it as a boost for the approach that many of their more conservative members support.
“The president has made clear what principles must be addressed if we are going to make a law instead of merely making political points,” Senator Mitch McConnell of Kentucky, the Republican leader, said Wednesday morning.
Speaker Paul D. Ryan of Wisconsin echoed that sentiment, saying that “the president did a very good job of putting a very sincere offer on the table. And that sincere offer that he put on the table should be the framework through which we come together to find a solution.”
While the president’s support of the Iowa Republican’s bill is not surprising, his vague promise not to support other bills is notable, as Mr. Trump told lawmakers last month that he would sign any immigration bill that Congress sends him. Republican leaders have said Congress should only pass legislation that Mr. Trump would sign, but how flexible the president would be was a key question for lawmakers.
The White House position was announced as the Senate began debate on immigration, which allows senators to build legislation from a blank slate on the Senate floor.
Other proposals with bipartisan support on Capitol Hill take a narrower approach than Mr. Grassley, extending protections for young immigrants brought to the country illegally as children and bolstering border security. But those bills do not include the tough changes to immigration law that Mr. Trump backs — and most Democrats strongly oppose.
The statement is likely to make deliberations on Capitol Hill far harder. The president ended an Obama-era program protecting young, undocumented immigrants, known as DACA, or Deferred Action for Childhood Arrivals, but gave Congress six months to find a legislative alternative. That deadline is now three weeks away.
The Grassley bill includes several measures to increase border security, including increasing the use of radar and tower-based surveillance, sensors and drones mostly along the Southwest border and increasing the number of border patrol agents. The National Guard would also be used to help constructs border fencing and operate some of the surveillance equipment.