President Trump sought to retake the reins of the immigration debate Thursday by announcing a bold plan to refashion legal immigration from its heavy reliance on family ties into a points-based system that would boost those with preferred skills.

Mr. Trump said the overall level of legal immigration would remain the same, at about 1.1 million people per year, but that the U.S. should do more to pick newcomers who would boost the economy rather than rely on migrants to pick themselves based on which relatives are already in the country.

Gone was the stiff rhetoric of the 2016 campaign, when candidate Trump warned of an “influx of foreign workers” and proposed a “pause” on job-based immigration. Instead, Mr. Trump talked of open doors and a nation of immigrants, though he said it matters how they get into the U.S.

“We want immigrants coming in. We cherish the open door,” he said in a speech in the White House Rose Garden. “But a big proportion of those immigrations must come in through merit and skill.”

Right now, only about 12% of immigrants are selected based on employment. The president said his plan would raise that to 57%, “and we’d like to even see if we can go higher.”

He said his plan would achieve 100% operational security at the border, with more technology to scan vehicles coming through the legal ports, more barriers to prevent people from jumping between the ports and tighter rules to stop abuse of the asylum system.

Yet Mr. Trump’s plan does not deal with future foreign guest workers, nor does it address any of the estimated 11 million illegal immigrants already in the U.S. who are clamoring for legal status.

Those omissions made the timing of the announcement curious.

Congress is debating what to do about the surge of migrants at the border, where nearly 110,000 people crossed illegally in April alone. The vast majority of those were families and unaccompanied children, setting a record.

Meanwhile, Democrats say they are less interested in legal immigration than they are in the 11 million illegal immigrants who they say should be rewarded with citizenship.

House Speaker Nancy Pelosi, California Democrat, said the president’s plan isn’t going anywhere on Capitol Hill, and she bristled at the claim that his points plan is based on merit.

“It is really a condescending word. Are they saying family is without merit?” she asked. “Are they saying most of the people who have ever come to the United States in the history of our country are without merit because they don’t have an engineering degree?”

Others were even more critical.

Senate Minority Leader Charles E. Schumer, New York Democrat, called Mr. Trump’s plan “anti-immigrant,” and United We Dream, an advocacy group for illegal immigrant “Dreamers,” said the plan was written by a “white supremacist.”

Immigrants’ List, a political action committee, said the president’s plan was intended to “rile up bigoted sentiment about immigrants.”

Those reactions didn’t jibe with Mr. Trump’s words, which cast his plan as evidence of an administration eager to embrace newcomers.

Far from shutting the door, he said, his plan would “increase the diversity of immigration flows.”

Still, the president painted immigration as a series of trade-offs.

He said bogus asylum seekers take assistance money from legitimate asylum seekers and are beginning to strain government finances.

He also said not tailoring the immigration system to merit means the most vulnerable low-skilled American workers face competition.

Mr. Trump drew audible cheers from his audience in the Rose Garden when he said his plan would speed up the point at which immigrants have to demonstrate that they have learned English and have a knowledge of American civics.

He said those will have to be proved “prior to admission.”

The president acknowledged the political difficulties of congressional action this year but signaled that he will take his plan to voters in his reelection campaign next year.

“We will get it approved immediately after the election when we take back the House, keep the Senate and, of course, hold the presidency,” Mr. Trump said.

Ali Noorani, executive director of the National Immigration Forum, broke with naysayers in the activist community. He saw Mr. Trump’s announcement as a good start for a broader dialogue.

“The administration’s plan recognizes that our country needs immigrants and that they contribute to economic prosperity and innovation across the U.S.,” he said. “That is a strong starting principle on which to build a conversation around fixing our immigration system.”

He said, though, that the U.S. economy needs workers “across all sectors,” so whatever emerges will need to be broader than what Mr. Trump has laid out.