DUBLIN — The top Catholic official in Northern Ireland’s power-sharing government abruptly resigned on Monday, plunging the territory into political uncertainty and adding to Britain’s complications as it plans to leave the European Union.

The official, Martin McGuinness, stepped down as deputy first minister to protest what he called the mishandling of a program that subsidizes the use of renewable energy to heat buildings.

Mr. McGuinness said he would not nominate a replacement, a decision that effectively sets off an election for the Northern Ireland Assembly, as it will end the current power-sharing agreement between Mr. McGuinness’s Catholic Sinn Fein party and the Democratic Unionist Party, which represents Protestants and is led by Arlene Foster, the first minister.

Under the 1998 Good Friday Agreement, which brought an end to the decades-long sectarian strife known as the Troubles, Catholics and Protestants share governance of the region, along with the British government.