WASHINGTON — President Trump demanded on Tuesday that a freshman lawmaker from Minnesota resign after she posted tweets deemed anti-Semitic even by fellow Democrats, but those tweets echoed some of the same insinuations about Jews and money that he has trafficked in for years, as a candidate and president.

Mr. Trump rejected the apology of Representative Ilhan Omar, one of the first two Muslim women elected to Congress, saying, “it was lame, and she didn’t mean a word of it.” Ms. Omar, he said, should leave the House or, at a minimum, give up her seat on a coveted committee.

“Anti-Semitism has no place in the United States Congress,” Mr. Trump told reporters during a cabinet meeting. “Congressman Omar is terrible, what she said. And I think she should either resign from Congress or she should certainly resign from the House Foreign Affairs Committee.”

Ms. Omar issued her mea culpa after a bipartisan storm of protest over the tweets, in which she said that the United States’ support for Israel was paid for with money from a pro-Israel lobbying group. “It’s all about the Benjamins baby,” she wrote on Twitter, referring to $100 bills.