“Of course we hope it will be enforced in a fair manner,” he said. “But the fact of the matter is we see Jewish students on college campuses and Jewish people all over being marginalized. The rise of anti-Semitic incidents is not theoretical; it’s empirical.”

David Krone, a former chief of staff to Senator Harry Reid of Nevada when he was Senate Democratic leader, has lobbied for years for such a policy change and praised Mr. Trump for taking action.

“I know people are going to criticize me for saying this,” Mr. Krone said, “but I have to give credit where credit is due.” He added, “It’s too important to let partisanship get in the way.”

Mr. Reid helped push for legislation similar to the order called the Anti-Semitism Awareness Act of 2016. It passed the Senate in December 2016 unanimously but died in the House as that session of Congress ended. It has been reintroduced by Democrats and Republicans but has made little progress to Mr. Trump’s desk.

Mr. Krone continued to work on the issue after Mr. Reid retired and reached out through a mutual friend last summer to Jared Kushner, the president’s son-in-law and senior adviser. The Jewish grandson of Holocaust survivors, Mr. Kushner embraced the idea, which also had been explored over the past year by the president’s domestic policy aides. With Mr. Kushner’s support, the White House drafted the order and Mr. Trump agreed to sign it.

Mr. Trump over the years has been accused of making anti-Semitic remarks, turning a blind eye to anti-Jewish tropes or emboldening white supremacists like those in Charlottesville, Va., in 2017. Just last weekend, he drew criticism for remarks in Florida before the Israeli American Council in which he told the Jewish audience they were “not nice people” but would support his re-election because “you’re not going to vote for the wealth tax.”

But he has also positioned himself as an unflinching supporter of Israel and a champion of Jewish Americans, moving the United States Embassy to Jerusalem, supporting settlements in the West Bank and recognizing the seizure of the Golan Heights. He also assailed Representative Ilhan Omar, Democrat of Minnesota, when she said support for Israel was “all about the Benjamins,” meaning money.