Democratic Majority for Israel is focused on raising support for Israel within the party, and the group and its allies worry that Mr. Sanders’s questioning of the Democratic Party’s longstanding support for Israel could damage the United States’ historically strong relationship with the country. But Mark Mellman, the group’s president, said it was equally worried about Mr. Sanders’s chances against Mr. Trump if he were to become the nominee.

In a statement, Faiz Shakir, Mr. Sanders’s campaign manager, condemned the ad and called on the rest of the Democratic presidential field to do the same.

“Every single Democratic candidate running for president needs to condemn these kinds of negative attack ads run by dark money groups,” he said. “It does not reflect the values of our party and it is not in the spirit of our issues-driven primary contest.”

He added, “But what our ​fund-raising ​numbers show is our supporters know the establishment will do anything to try to stop Bernie, and they’re ready to rally to his side at a moment’s notice.”

The campaign said its fund-raising haul came from more than 70,000 donations.

Lisa Lerer contributed reporting from Ames, Iowa, and Shane Goldmacher from Des Moines.