The UK has moved to the 'delay' phase of the battle against coronavirus, Prime Minister Boris Johnson says.
Ten people have died in the UK - and health officials have expressed concerns that up to 10,000 people could be infected with Covid-19.
Boris Johnson has described it as "the worst public health crisis for ageneration".
It comes after Taoiseach Leo Varadkar announced a shutdown of schools in the Republic of Ireland, due to the pandemic.
Speaking from the US on Thursday morning, the Fine Gael leader said all schools, colleges and childcare facilities will close until 29 March.
One patient has died from Covid-19 in the Republic. There have been 70 positive tests.
Following a meeting on Thursday evening, the First and deputy First Minister said schools in Northern Ireland will remain open at this stage.
Meanwhile the Public Health Agency has confirmed a further two cases in Northern Ireland, bringing the total up to 20.
"Both cases are adults and both were secondary transmissions," the PHA said, adding that a total of 279 tests have now been carried out here.
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Mr Varadkar said teaching will be done online or remotely, while State-run "cultural institutions" will close and indoor gatherings of more than 100 people and outdoor meetings of more than 500 will be cancelled.
Anyone entering Ireland will be informed of the measures and asked toself-isolate if they are displaying symptoms, the Irish premier added.
Working from home will be encouraged, but where people do congregate in offices break times should be "staggered".
The Taoiseach said meetings should be done remotely but restaurants, cafes and other businesses can stay open.
"People should seek to reduce social interactions as much as possible," he added.
NI's leaders said they are taking part in the UK's plan to delay the spread of coronavirus by encouraging self-isolation for anyone who feels unwell.
First Minister Arlene Foster and deputy First Minister Michelle O'Neill have not ordered the closure of schools.
Mrs Foster said: "The timeliness of intervention is very important and that iswhy the science and the evidence is important."
She added that it was "disappointing" that she had no prior notice of what the Irish government was going to do.
Ms O'Neill acknowledged the separate approach from the Republic, with its open land border with Northern Ireland, was confusing to some.
In a statement, the GAA confirmed it would be suspending all activity at club, county and educational levels until 29 March.
The organisers of rugby's Pro14 said the season would be suspended.
Sinn Féin President Mary Lou McDonald said it was taking a number of steps in response to Covid-19, including cancelling Easter commemorations.
She said: “This is going to be a very challenging period and we all need to pull together to get through it.”
Deborah McAleese reports on the Covid-19 impact:
The Health Service has issued new advice on hospital visits.
A spokesperson said: "It is important to emphasise that there is no blanket ban on visits to hospitals or other care settings at this stage.
"It is fully accepted that for many families and patients, visits are essential and important to patient wellbeing.
"Given the particular risks from coronavirus, hospitals and other providers have to prioritise the safety and wellbeing of patients and staff.
"People with underlying health problems are at particular risk, which is why hospital environments and care homes need to take particular care."