He paired the address with his first naturalization ceremony at the White House, a move intended to underscore the idea that he supports legal immigration. And his language was markedly different; instead of insisting on the “big beautiful wall” he promised during his 2016 campaign, Mr. Trump took care to use the word “barrier” as well — and seemed to pare back his vision for it.

Calling the wall “a powerful and beautifully designed see-through steel barrier on our southern border,” Mr. Trump said: “This is not a 2,000-mile concrete structure from sea to sea. These are steel barriers in high priority locations. Much of the border is already protected by natural barriers such as mountains and water.”

Mr. Trump noted that he had adopted some Democratic proposals on border security. The president proposed $800 million for humanitarian assistance and $805 million for drug detection technology, in addition to funding for 2,750 more border agents and law enforcement officials and 75 new immigration judge teams.

In her talking points, issued to Democrats, Ms. Pelosi said her party favored “new drug, weapons and contraband scanning technology at official ports of entry,” and “filling the more than 3,000 vacancies for customs officers.” Ms. Pelosi also intends to bring up legislation in the coming days that includes an additional $1 billion for border security, including $563 million for 75 new immigration judges and support staff.

Even so, Democrats roundly criticized the president’s plan. They were particularly incensed that Mr. Trump’s offer extended protections to Dreamers and T.P.S. recipients that he himself revoked. And they said the deal was a nonstarter because it did not offer any permanent protections for Dreamers.

“I think it’s simply more fake promises raising false hopes,” Senator Richard Blumenthal, Democrat of Connecticut, said. “It will fool few Americans because it’s neither serious nor credible as a real remedy for Dreamers.”