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Britain has no formal succession plan should the leader become incapacitated, but Johnson asked Foreign Secretary Dominic Raab to deputise for him.
The 55-year-old was admitted to hospital on Sunday night and had been undergoing tests after suffering persistent coronavirus symptoms, including a high temperature, for more than 10 days.
Downing Street had said he was in good spirits and still in charge, though on Monday night (local time) he was moved to an intensive care unit - where the most serious cases are treated - at St Thomas' hospital in central London.
Johnson had been given oxygen, a source said.
"Over the course of this afternoon, the condition of the Prime Minister has worsened and, on the advice of his medical team, he has been moved to the Intensive Care Unit at the hospital," a spokesman for his office said.
"The PM has asked Foreign Secretary Dominic Raab, who is the First Secretary of State, to deputise for him where necessary," Downing Street said. "The PM remains conscious at this time."
Downing Street said he had been moved to the intensive care unit as "a precaution should he require ventilation to aid his recovery".
The Queen had been kept informed by Downing Street, Buckingham Palace said.
Johnson tested positive for the virus on March 26 but after 10 days of isolation in an apartment at Downing Street, he was still fighting the virus on Sunday evening with a high temperature and persistent cough.
His spokesman had earlier refused to answer directly after being asked whether he had pneumonia. But his move to intensive care confirmed the gravity of the situation.
"There is no doubt this turn of events means Boris Johnson is extremely sick," said Derek Hill, a professor of medical imaging at University College London.
"One of the features of COVID-19 in all countries seems to be that many more men become seriously ill than women - especially in the over 40 age group. Also we know that people under about 60 seem to have a higher chance of making a recovery from critical illness with COVID-19 than older people."
British and world leaders wished Johnson well.
"I send all my support to Boris Johnson, to his family and to the British people at this difficult moment," said French President Emmanuel Macron. "I wish him a speedy recovery at this testing time."
Theresa May, Johnson's predecessor as Prime Minister, said: "My thoughts and prayers are with Boris Johnson and his family as he continues to receive treatment in hospital."
Johnson's pregnant 32-year-old fiancée, Carrie Symonds, also had symptoms but said on Saturday she was feeling better.
Raab, the 46-year-old son of a Czech-born Jewish refugee who fled the Nazis in 1938, was brought up in the southern English region of Buckinghamshire and studied law at Oxford University before becoming a lawyer working on project finance, international litigation and competition law.
A karate black belt, he was appointed as foreign minister in Johnson's first cabinet after the Prime Minister took office in July 2019.
Asked at a news conference earlier on Monday whether he had been in touch with Johnson by either text or by telephone, Raab said he had last spoken to the Prime Minister on Saturday.
On March 27, Johnson became the first leader of a major power to announce that he had tested positive for COVID-19.
Medics said patients with COVID-19 can deteriorate after about 10 days, with some developing pneumonia. National Health Service guidelines advise those who are self-isolating not go to hospital unless they develop new symptoms or become sufficiently unwell.
Johnson, who is not a smoker, said recently that he wanted to lose weight. He plays tennis and while mayor of London used to cycle around the capital.
The face of the 2016 Brexit campaign, he won a resounding election victory in December last year before leading the United Kingdom out of the European Union on Jan. 31.
He has faced criticism for initially approving a much more modest response to the new coronavirus outbreak than other European leaders, saying on March 3 that he had been shaking hands with coronavirus patients.
He changed tack when scientific projections showed a quarter of a million people could die in the United Kingdom. On Monday, health officials said Britain's death toll stood at 5373.
Johnson effectively shuttered the world's fifth-largest economy, advising people to stay at home and the elderly or infirm to isolate themselves for weeks.