President Biden will face another round of organized protest votes over his wartime support for Israel on Tuesday, when New York and three other states hold presidential primaries.

The outcome of the contests is not in doubt for Mr. Biden. But activists infuriated over his handling of the war in Gaza are urging participants to vote “uncommitted” or leave ballots blank to maintain pressure on the president.

They have put particular emphasis on New York, a large Democratic state that has been a center for demonstrations against the war, including one during a star-studded Biden campaign fund-raiser last week.

Unlike other states, New York does not allow participants in its primary to vote “uncommitted” or write in other options. So organizers have urged voters to register their disapproval of Mr. Biden by leaving their ballots blank instead.

The “Leave It Blank” campaign has the support of the local Democratic Socialists of America and the Working Families Party, New York’s influential left-leaning party. But two of the president’s most trenchant Democratic critics around the war, Representatives Jamaal Bowman and Alexandria Ocasio-Cortez of New York, have not promoted it.

Antiwar activists argue that the “uncommitted” protests, which began in Michigan in February, have had an effect. After offering Israel unflinching support in the aftermath of Hamas’s deadly attack on Oct. 7, Mr. Biden has grown more openly critical of the American ally’s war strategy in recent weeks. The humanitarian crisis in Gaza has also accelerated after months of Israeli bombardment.

Groups are organizing similar votes in three other states holding primaries on Tuesday. In two of them, Connecticut and Rhode Island, primary participants will have the option of voting “uncommitted” if they want to register a protest against the president. In Wisconsin, a crucial swing state, they can choose a similar label, “uninstructed,” to show concern.

In another twist, neither Mr. Biden nor his critics are likely to know the size of the protest vote in New York on election night.

A spokeswoman for New York’s Board of Elections said the body did not typically report the number of blank ballots cast in presidential primaries in initial, unofficial results because they have no effect on the allocation of party delegates.

Organizers of the “Leave It Blank” campaign have threatened to sue the board to pressure it to share the result more quickly. But on Monday, the spokeswoman, Kathleen McGrath, said the board had no reason to change its practice. She said the tally of blank ballots would be public within two weeks.