The meeting of senior officials will be the first attended by the prime minister since the virus emerged, with 19 people in the UK having contracted the illness so far.
Speaking after a meeting with chief medical officer Chris Whitty and health secretary Matt Hancock, Mr Johnson said the outbreak was now "the government's top priority".
Challenged over why he was waiting three days to call the Cobra meeting, he said: "We have just had a meeting of all the government ministers concerned and there has been a regular series of Cobra meetings to prepare for this eventuality.
"I think people are right to be concerned and they are right to take every possible precaution and we will in the course of the next few days be issuing further advice about how to respond and how we will be deal with any potential outbreak.”
Mr Johnson expressed his sympathy for the family of the first British victim of the outbreak, who had been a passenger on the quarantined cruise liner Diamond Princess in Japan.
Asked why the UK had not acted more quickly to bring UK nationals home from the ship, he said: "Obviously, we very much regret the loss of life of the individual concerned but we think that the best thing to do is not to move people around too much in the current situation.
“Not to repatriate unless you can be absolutely sure there is not going to be a spread or contagion to this country, that’s the principle we are adopting.”
Mr Johnson added: "I just want to reassure everybody and say that the NHS is making every possible preparation.
“As you can imagine, the issue of coronavirus is something that is now the Government’s top priority.
I just really want to repeat the advice of the chief medical officers, which I think is the best thing to get across – the most valuable thing we can all do to prevent the spread of the coronavirus is to wash our hands for 20 seconds or more with hot water and soap.
“That’s the best single piece of advice we can give."
Earlier on Friday, Dr Frank Atherton, the chief medical officer for Wales, confirmed the first case of coronavirus in the region, saying the patient had recently returned to Wales from northern Italy, where they contracted the virus.
A World Health Organisation (WHO) spokesman also said that the outbreak is "getting bigger", with the possibility that it will reach further countries, "if not all countries".
Mr Johnson was working in Downing Street on Friday and will be at his country residence Chequers over the weekend. A Downing Street spokesman gave no explanation of why the Cobra meeting was not being held earlier, but said that so far during the outbreak there had been one meeting a week led by the health secretary Matt Hancock.
The prime minister last night visited Kettering Hospital in Northamptonshire to discuss preparations for possible coronavirus cases with senior clinicians.
Mr Johnson joined the night shift and stayed at the hospital from 11pm to 3am, spending time with staff in the accident and emergency department, intensive care unit and paediatrics ward, said Downing Street.
“Staff talked him through the processes in place for if there is a suspected case,” said the spokesman.
He said that, on top of Cobra sessions, there had been daily meetings during the coronavirus outbreak bringing together Public Health England, the Department of Health, the chief medical officer, chief scientific officer and other government departments. Mr Johnson had been kept updated throughout, he said.
George Osborne, the former Tory chancellor, said the government “now needs to onto a ‘war footing’ with the coronavirus” and hold daily NHS press briefings, regular Corba sessions chaired by the prime minister and ministers on all major media shows.
“The public is fearful, wants information and needs to know their leaders have got a grip,” he added.
Labour’s Jonathan Ashworth added: ““Our part-time prime minister needs to get a grip of this escalating situation quickly. It shouldn’t take another three days for this meeting to take place.
“People are understandably worried. Boris Johnson should drop his childish ban on ministers appearing on BBC radio programmes. The public deserves to hear what plans are in place to deal with the outbreak.”
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