The PSNI is "looking at funerals" where large numbers of people gathered in breach of social distancing rules, Arlene Foster said yesterday.
However, a senior police officer told Stormont's justice committee earlier that specific guidelines for carrying out enforcement action at funerals was never issued by the Executive.
There has been criticism of police on social media following the emergence of pictures showing large crowds attending some funerals. Several republican funerals saw big crowds in clear breach of social distancing rules.
Assistant Chief Constable Alan Todd said policing at funerals is "difficult" due to a lack of specific instructions in the coronavirus regulations.
He told MLAs: "Funerals are a hugely emotive and emotionally sensitive time for everybody involved.
"There's been a lot of public discourse from a whole lot of angles about funerals. What's permissible or not, what is guidance or not is a matter for the legislators and the Executive.
"Police are generally operating in a space where there is no legislation, not a lot of guidance and trying to apply some common sense to bring about a successful outcome."
Mr Todd said he is not sure anyone would think that police taking a "hands on" approach to enforcement at a funeral would be "a good idea".
Mr Todd said he has not issued guidelines to officers around funerals "because there are no guidelines issued from the people who laid the regulations".
He added: "They're not committing any offence under regulation six, but they shouldn't have been travelling under regulation five.
"You can see the difficulties and trying to make some decisions around that."
Speaking later at yesterday's Executive press conference, First Minister Mrs Foster said "clearly they shouldn't be gathering in large crowds at funerals".
She added: "It is very clear that only up to 10 people should be attending those funerals, and I know that the police are looking at those funerals where there have been an excess of that number and files will be sent to the Public Prosecution Service around those issues.
"Look, we recognise this isn't easy for anybody.
"It's certainly not easy when people are grieving to have to try and abide by these rules and regulations."
Agriculture Minister Edwin Poots said he would like to see the Executive consider allowing more than 10 people to attend a funeral.
Speaking on Radio Foyle yesterday, the DUP MLA, whose father died recently, said: "Most families in Northern Ireland have more than 10 people in close connection.
"I just think, personally, it is a very cruel thing to turn round and say that a son-in-law or daughter-in-law could not attend a funeral, that a grandchild cannot attend a funeral, and pick out members of a family that cannot attend a funeral."