There have been no Covid-19 related deaths reported by Northern Ireland's Department of Health in the past 24 hours.
It is the first day since 18 March - almost 10 weeks ago - that no deaths have been reported in Northern Ireland.
The latest figures from the department state the total number of people who have died remains the same as Monday's total of 514 deaths.
Health Minister Robin Swann said it was "a clear sign of progress".
"We all have been waiting for a day like this," he told Stormont's daily press conference on Tuesday.
Although there was a clear downward trend, there were "no grounds for complacency", he added.
"If people get it into their heads that this emergency is over, the consequences will be catastrophic," he said.
Complacency, said the minister, would be an "insult to those who have lost their lives and to those mourning them".
"A second wave of the virus is also expected in the months ahead so we must keep our defences up," he added.
He said a fourth testing site as part of the UK's national testing programme would be opened in Enniskillen later this week.
The minister said the easing of some lockdown restrictions meant there were now more "legitimate reasons" for people to be out of their homes, but said they should not forget the basic guidance.
He addressed ongoing concerns about Covid-19 in care homes and said 5,603 residents have now been tested, with more than 5,000 staff tested as well.
Deputy First Minister Michelle O'Neill said she was heartened by the report of no new deaths.
"Let's keep working together to have more days like this," she tweeted.
In the Republic of Ireland, nine people with Covid-19 have died since Monday, a day where the country recorded no new Covid-19 linked deaths.
There have now been a total 1,615 coronavirus-related deaths in the country.
In other developments on Tuesday:
- Finance Minister Conor Murphy warns some Stormont departments could run out of cash this summer
- Methodist College says it can only have a "meaningful" reopening if social distancing guidelines change
- Expiring driving licences are to be extended by seven months
- The Irish government says Taoiseach Leo Varadkar was following guidelines when he was photographed with friends having a picnic
The total number of confirmed cases of coronavirus in Northern Ireland now stands at 4,637 - an increase of 28 on Monday's figures.
The Department of Health's dashboard also says there are 69 active outbreaks of Covid-19 in NI care homes.
These figures are one of two sets published in Northern Ireland.
The other are weekly statistics from Northern Ireland's Statistics and Research Agency (Nisra), which cover all fatalities where coronavirus has been recorded on the death certificate.
The latest Nisra figures show 664 deaths had occurred by Friday 15 May:
- 303 in care homes
- 322 occurred in hospital
- 33 at home or other and six in hospices
There is a considerable difference in the death tolls in the two sets of figures: the Department of Health - which records deaths of patients who tested positive for coronavirus and therefore mostly died in hospital - had only recorded 472 deaths by 15 May.
On Monday, the Republic of Ireland also reported there had been no Covid-19 related deaths in the past 24 hours, news welcomed by Chief Medical Officer Dr Tony Holohan as "part of the downward trend".
There have been a total of 1,606 coronavirus-related deaths in the Republic of Ireland.
A further 59 new confirmed cases brings the country's total to 24,698.
Fewer deaths related to coronavirus were registered in the UK in the week to 15 May, than in any week since the beginning of April.
Between 11 and 15 May, there were 4,210 death registrations mentioning Covid-19.
Down from 4,426 the previous week, it is the lowest weekly figure since the 3,801 for the week ending 10 April.
Coronavirus accounted for just over 25% of all deaths in the UK in the week to 15 May.