Ms. Wiley was well to the left on many important policy issues, including policing and education. Both candidates would be New York’s first female mayor, while Ms. Wiley would become the first Black woman mayor.

“I said on election night, we must allow the democratic process to continue and count every vote so that New Yorkers have faith in our democracy and government,” Ms. Wiley said in a statement on Tuesday. “And we all must support its results.”

Many progressive voters didn’t like Mr. Adams as a former Police Captain and relative moderate on several key issues.

Early results suggested that Adams had considerable strength among working class voters of color and some traction within white voters with moderate views.

I. Daneek Miller is a City Councilman who supports Adams. He proposed Tuesday via text that the system had given way to “an attempt at eliminating the candidate of moderate workers people and traditionally marginalized community” in an effort to get a new referendum. This implicitly criticizes the Yang-Garcia Alliance.

“It is incumbent upon us now to address this issue of ranked voting and its use against a large portion of the public,” stated Mr. Miller, Co-Chair of Black, Latino and Asian Caucus.

Other close observers also expressed concern at the decision to release a rank-choice tally, without accounting absentee voting.

“There is a real risk that voters will believe a series of facts about the races that will be disproven after all votes are in,” said Ben Greenfield (a senior survey data analyst at Change Research), who conducted polling to support a pro-Garcia PAC. “This could make a confusing system more confusing, increase mistrust and take the risk of creating a new one.

Reporting by Dana Rubinstein; Jeffery C. Mays; Anne Barnard; Andy Newman; and Mihir Zaveri