LONDON — Prime Minister Boris Johnson of Britain was discharged from the hospital on Sunday, a major step forward in his recovery from the coronavirus and a welcome relief for a nation whose political leadership has been harder hit by the contagion than that of any other Western country.

Mr. Johnson, who spent three nights in intensive care at St. Thomas’ Hospital in London, will convalesce for some time at Chequers, the prime minister’s country house, the government said in a statement. But he will soon be able to sign off on major decisions, including when to ease the country’s lockdown.

In an emotional five-minute video, Mr. Johnson thanked the country’s National Health Service, declaring it had “saved my life, no question.”

Wearing a suit and tie, but looking and sounding fatigued, Mr. Johnson singled out two nurses from New Zealand and Portugal who, he said, had kept a vigil over him “when things could have gone either way.”