The primary contest has been one of New York City’s most chaotic in recent years. It effectively began last fall with the federal corruption indictment of the current mayor, Eric Adams, a Democrat. The Trump administration later dropped the charges, but Mr. Adams opted out of the primary to run for re-election as an independent.

Sunday, several major cities including Washington, D.C. and New York City began boosting their police presences outside some religious, cultural and diplomatic sites.