DUP minister Edwin Poots should apologise for saying coronavirus is more common in nationalist areas, Sinn Féin's John O'Dowd has said.
Last week, Mr Poots said the difference in transmission between nationalist and unionist areas was "around six to one".
He has also criticised new lockdown restrictions imposed by the executive to manage the virus.
Mr O'Dowd said his comments about virus levels in different council areas were a "disgrace" and should be withdrawn.
The Department of Health said it was vital to stress that Covid-19 represented "a threat to everyone in society, regardless of their background, and that it is spreading across the community" in Northern Ireland.
"For the record, data on Covid infections is not collected according to religious or political affiliation," it added.
A further six Covid-19 related deaths have been reported in Northern Ireland by the Department of Health, bringing its total to 621.
The department also reported an additional 820 positive cases of the virus, meaning there have been 28,040.
There were 3,869 individuals tested in the previous 24 hours.
Mr O'Dowd's comments came after Mr Poots, the agriculture minister, had spoken to UTV on Friday, openly criticising the imposition of the new regulations, which are in place for the next four weeks.
"I will abide by the regulations, as have most people in my community," said Mr Poots.
"What I'm saying is, those people who didn't abide by them, including the Sinn Féin leadership - because a lot of this started shortly after the Bobby Storey funeral.
"A lot of the problems started after that event, and people in that community saw the breaking of the rules.
"That's why there is a difference between nationalist areas and unionist areas - and the difference is around six to one."
The remarks have drawn criticism from other political parties at Stormont.
On Sunday, Mr Poots was defended by his party colleague, Education Minister Peter Weir, who said "people have a right to express their opinions".
According to the latest Department of Health data, there are now 261 hospital inpatients being treated for Covid-19, compared to the peak of the first wave in April, when there were 322 people in hospital.
There are 29 people in intensive care, with 25 of them ventilated.
There are also 80 outbreaks of Covid-19 in care homes across Northern Ireland.
The Derry and Strabane area, which at one point had the worst infection rate in the UK, has seen numbers decrease and is now at 769.9 cases per 100,000 over a seven day period.
Today 6 people have died as a result of Covid. My thoughts are with the families bereaved.— Michelle O’Neill (@moneillsf) October 19, 2020
It is evident that the covid situation is deteriorating rapidly. The next four weeks are critical and we all need to work together to try and gain back some control. #WashYourHands
Health Minister Robin Swann appealed for members of the public not to become "distracted" and to adhere to public health messages on social distancing and reducing contacts.
"Unfortunately, the predictions that were made about the increase in cases and the consequences this will bring are coming true," he said.
Deputy First Minister Michelle O'Neill tweeted: "It is evident that the covid situation is deteriorating rapidly," she said.
"The next four weeks are critical and we all need to work together to try and gain back some control."
DUP 'must stand by executive decisions'
Speaking to BBC Radio Ulster's Talkback programme on Monday, Mr O'Dowd condemned the comments by Edwin Poots.
"His comments about the breakdown of the council areas and his hint that this is a Catholic problem is an absolute disgrace," he said.
"(They are) comments that he should withdraw - and comments he should apologise for."
Alliance MP and the party's deputy leader, Stephen Farry, also called for an apology.
"People found it deeply offensive - the onus has to be on an apology," he told Talkback.
"The DUP have an absolute lock on decision-making, nothing ever comes to the executive table or leaves it without the DUP's full agreement, so people are scratching their heads as to how last Tuesday the DUP could be saying one thing in the executive and then seeing a key minister peeling off in that way."
However, former DUP assembly member Nelson McCausland said Mr Poots' views had been misrepresented.
He said in Great Britain it was pointed out at an early stage that there was a higher incidence of coronavirus in black, Asian and minority ethnic (BAME) groups.
"No-one's saying that's racist - those are legitimate questions for people to ask and in fact it's important that they are asked," he said.
He said it was important to establish if there was a social reason as to why somewhere like Derry and Strabane had such a high rate of infection.
Sinn Féin's Mr O'Dowd also defended actions of his colleague, Communities Minister Carál Ní Chuilín, after she called for all sporting events to be played behind closed doors.
The regulations do not prohibit spectators attending outdoor sporting events, and First Minister Arlene Foster tweeted that it was "preposterous" for sports clubs to be told anything to the contrary.
Mr O'Dowd said he believed Ms Ní Chuilín had taken "responsible action" by urging sports clubs to hold events without spectators.
"She wrote directly to sports clubs and she'll be meeting them in the next few days to discuss this further," he added.
"How the joint first ministers choose to respond is up to them - there are protocols and avenues in place for those discussions to take place other than on Twitter."