Michelle O'Neill has said she stands over her actions at Bobby Storey's funeral but admitted that a selfie taken at Milltown cemetery "should not have happened".
The Sinn Fein vice president made clear to MLAs that she would not be quitting following the controversy over the large crowds that gathered in west Belfast for the event yesterday.
She also declined to apologise to anyone who might have contracted Covid-19 as a result of being among the crowds yesterday.
The Deputy First Minister told members of the Executive Committee that the things the organisers could control - such as the size of the cortege and the numbers inside the church - were observed.
Ms O'Neill insisted the cortege was limited to 30 while social distancing inside the church was "exemplary". It is understood more than 100 people were inside the church.
Contention surrounds the fact the guidelines Sinn Féin has cited in regard to observing yesterday's funeral service are still in draft format, and have not been formally signed off by the powersharing executive.
The draft guidance allows more people to attend church services than the limit of ten that applied earlier in the lockdown.
However, the Diocese of Down and Connor has confirmed that its churches should still have been applying the 10 number restriction to funerals yesterday.
A statement from the diocese said it received updated guidance from The Executive Office yesterday evening.
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"I can stand over my actions," Ms O'Neill told MLAs.
"I have led through this pandemic from the front, I will continue to lead from the front and I continue to work within the regulations and encourage everybody to stick within the regulations and the guidance as we have set out."
She added: "I do think it's unfortunate that a lot of the charges that are being levelled towards me are political points scoring, as opposed to actually being about the rules.
"But that's not to take away, I am being very clear, to anyone who's lost throughout this pandemic, this has been an absolute nightmare."
The Sinn Féin vice president added: "I can only control what's within my gift."
She said her party's actions, such as live streaming the funeral and putting stewards on the roadside to stop people joining the cortege, had prevented the crowds reaching many thousands.
At points the hearing, which was supposed to be focused on the coronavirus response, turned into pointed exchanges between unionist and republican members about Mr Storey's past and the origins of the Troubles.
Ms Foster interjected after one such exchange.
Noting her own family's experience of the Troubles, she added: "We could all sit here and reminisce about things that have happened in the past.
"We're supposed to be talking about the Covid-19 regulations, and how they have impacted on the people of Northern Ireland."
Giving evidence alongside Ms O'Neill, the DUP leader voiced concern about the impact of the funeral scenes on Stormont's public health message.
"I think the credibility of that message has been severely damaged as a result of what happened yesterday," she said.
Ahead of the committee hearing, Mrs Foster said Ms O'Neill and other Sinn Féin members who attended had sent out a message of "do as I say and not as I do".
"She needs to apologise and recognise the wrong that has been done, and she absolutely needs to make amends for what happened yesterday and take steps to try and build up that credibility again," Ms Foster said.
"Many people have had to go to through mourning and grief during this time and haven't had the comfort of people coming to their homes, they haven't had the comfort of a full service, yesterday they asked 'well, why was that the case?"'
Ms O'Neill said a selfie photograph that was taken of her and two other attendees at the funeral "should not have happened".
She said it happened in the "blink of an eye" at the close of the commemoration at Milltown cemetery.
"That should not have happened and I am absolutely OK to say that," she said.
Two metres social distancing an' all that there.. but since when did become acceptable to take a selfie at a funeral? pic.twitter.com/hF33jSWSOq
— Brendan Hughes (@brendanhughes64) June 30, 2020
