A group of Democrats in Michigan is urging voters unhappy with President Biden’s approach to the war between Israel and Hamas to vote for Uncommitted on the state’s Feb. 27 primary ballots to demonstrate a frustration that Mr. Biden has not demanded a cease-fire in the conflict.

The effort, called Listen to Michigan, is set to be formally announced on Tuesday. The campaign is being run by Layla Elabed, a community organizer from Dearborn, Mich., who is the younger sister of Representative Rashida Tlaib of Michigan. The campaign’s budget will be $250,000 and will include digital advertising, direct mail and phone and text banking to contact supporters, Ms. Elabed said.

“We’re a voting bloc,” she said. “We have the political power to really shift Biden’s election. We did it in 2020.”

The group’s website is blunt. “Tell Biden, count me out for genocide,” it reads.

There is a history of Michigan Democrats using Uncommitted as a protest vote. In 2008, when Michigan defied Democratic National Committee rules by moving its primary up in the nominating calendar, Barack Obama’s campaign urged supporters to vote for Uncommitted against Hillary Clinton. In that contest, 40 percent of Democratic primary voters chose Uncommitted against Mrs. Clinton and three other candidates.

Mr. Biden is not likely to be seriously challenged in Michigan’s primary by Representative Dean Phillips of Minnesota or Marianne Williamson, the author, who are both on the ballot. Mr. Biden won the party’s first recognized primary, on Saturday in South Carolina, with 96 percent of the vote. But there is ample polling evidence that his position in support of Israel as it wages war on Hamas in the Gaza Strip is unpopular.

An NBC News poll released Sunday found just 29 percent of voters approved of Mr. Biden’s handling of the war between Israel and Hamas — including just 15 percent of voters younger than 35. Among Democrats, the poll found that 44 percent approved of Mr. Biden’s handling of the war in Gaza, while 45 percent disapproved.