The Prime Minister, who was taken to hospital on Sunday, praised the "brilliant" NHS staff as he vowed to "work with his team to fight this virus".
He tweeted: “Last night, on the advice of my doctor, I went into hospital for some routine tests as I’m still experiencing coronavirus symptoms.
"I’m in good spirits and keeping in touch with my team, as we work together to fight this virus and keep everyone safe.
“I’d like to say thank you to all the brilliant NHS staff taking care of me and others in this difficult time. You are the best of Britain.
Last night, on the advice of my doctor, I went into hospital for some routine tests as I’m still experiencing coronavirus symptoms. I’m in good spirits and keeping in touch with my team, as we work together to fight this virus and keep everyone safe.— Boris Johnson #StayHomeSaveLives (@BorisJohnson)April 6, 2020
"Stay safe everyone, and please remember to stay at home to protect the NHS and save lives.”
His update came as Downing Street dramatically accused foreign agents of spreading “falsehood and rumours” about the Prime Minister’s health.
Mr Johnson's official spokesman hit out after a state-backed Russian news agency reported inaccurately that Mr Johnson had been put on a ventilator.
“That is disinformation,” said the Prime Minister’s official spokesman, making clear the allegation was untrue.
He went on: “Our specialist government units have seen a rise in false and misleading narratives since the coronavirus pandemic started. It is vital that any disinformation is knocked down quickly. DCMS and the Cabinet Office continue to work closely with social media companies to press for action to stem the spread of falsehoods and rumours.”
No 10 said Mr Johnson was “in good spirits” and had had “a comfortable night” at St Thomas’s hospital where is undergoing tests. He has been “in contact with” No 10 colleagues and had been sent red boxes of official papers, they added, making clear he could not be on a ventilator.
The spokesman made no comment on a Times report that the PM had been given oxygen.
Culture Secretary Oliver Dowden is also asking social media firms to crack down on the circulation of a “crazed conspiracy theory” linking 5G phone masts to the spread of coronavirus.
“The Secretary of State is due to speak with some of the big social media firms later on this week to be very clear about the need to stop the spread of what is a crazed conspiracy theory. You have seen reports of criminal vandalism against 5G masts. People need to understand that by destroying these masts, they’re actually putting lives at risk because these are masts which emergency responders rely upon.”
Separately, the Culture Select Committee is asking new Ofcom boss to probe concerns that state-backed news agencies are “disseminating false narratives” about Covid-19 through social media in order to circumvent broadcasting regulations.
Committee chair Julian Knight said: “To hear that crackpot theories are leading to people attacking phone masts or threatening telecom workers is sickening and it’s clearly time to act.
“We’ve called on the Government to work with social media companies to stamp out deliberate attempts to spread fear about COVID-19 and it is right that they are being called to account for allowing disinformation on their platforms.
“We’re also calling on Ofcom to investigate whether international news organisations are using social media to disseminate state-backed disinformation on COVID-19 in order to get around UK broadcasting regulation.”
Downing Street also insisted Mr Johnson will follow doctors’ advice when pressed on whether it was safe for the Prime Minister to continue working while in hospital.
“The PM, as I said, will of course be guided by the advice of doctors,” his official spokesman said.
“The position is that the PM remains in charge of the Government.”
Meanwhile, No 10 adviser Dominic Cummings is yet to return to work after going into self-isolation with symptoms in line with coronavirus.
“He is not back in No 10 today. He is in contact with No 10,” the Prime Minister’s official spokesman said.