President Trump during a meeting with members of Congress at the White House on Tuesday.

Tom Brenner/The New York Times

WASHINGTON — President Trump announced his support on Wednesday for the immigration legislation drafted by Senator Charles E. Grassley to codify his own plan, and said that he would oppose bills that “fail to deliver for the American people.”

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 holds a rare open debate on immigration, which…

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