LAS VEGAS — President Trump on Saturday again declared that the United States was “full” and called its asylum system “a scam,” tying his push to close the country’s borders to undocumented immigrants and asylum seekers to an entreaty for Jewish voters to support his re-election campaign.

“Our system’s full; our country’s full,” Mr. Trump said, speaking to an audience that included descendants of Holocaust survivors, Jews in red skullcaps emblazoned with “Trump” in white thread and people carrying Israeli flags. “You can’t come in. Our country is full. What can we do? We can’t handle any more. Our country’s full. You can’t come in, I’m sorry.”

He was met with raucous applause and cheers at the Republican Jewish Coalition’s annual leadership meeting in Las Vegas, underscoring how many conservative Jewish voters, alarmed by rising threats of anti-Semitism and energized by his pro-Israel policies, have embraced a president with a history of trafficking in anti-Semitic tropes — including remarks that he has made before the coalition.

Fresh from a visit on Friday to a California border town, the president doubled down on his attacks on migrants seeking asylum at the border. The administration has recently toughened its policy for accepting asylum seekers, with stories of fleeing violence and corruption no longer meeting the standard for entry.