ALBANY, N.Y.—New York’s top court ordered the state to draw new congressional district boundaries ahead of the 2024 elections, eliminating lines drawn for 2022 that Republicans sought to keep.

The ruling could boost Democrats in the closely divided House of Representatives, which currently has 221 Republicans and 213 Democrats. Both parties were already girding for several contested seats in New York, where five districts had been rated as tossups by the nonpartisan Cook Political Report.