LONDON — Mark J. Carney, the governor of the Bank of England, will stay in his role until the end of January 2020, the government said on Tuesday, which means that he would run the central bank for 10 months after Britain’s departure from the European Union.

Mr. Carney, who has been governor of the central bank since 2013, has been sharply criticized in recent years by supporters of Britain’s exit from the bloc, a process known as Brexit. They accuse him of taking partisan positions against the country’s withdrawal and of politicizing the bank before the June 2016 referendum in which Britons voted to leave the European Union. His most ardent opponents, led by the Conservative lawmaker Jacob Rees-Mogg, have called on him to resign.

The bank governor’s supporters, however, argue that Mr. Carney warded off a recession with his leadership after the referendum. They laud his calm and collected demeanor. Because he is Canadian, they say, he is a credible outsider with no skin in the game.

The leader of the Bank of England is typically appointed to an eight-year term, but Mr. Carney, a former Goldman Sachs banker, repeatedly said he would leave in 2018, citing family commitments. After the Brexit vote, he revised that stance, saying he would stay until the summer of 2019 to provide stability at the central bank.