Police are investigating a second gathering at a republican funeral.
Pictures posted on social media for the funeral of republican activist Patricia Campbell showed a large group of people follow the coffin through the streets of Turf Lodge in Belfast.
Police acknowledged how traumatic a time a funeral can be but said it was essential that people respect the current health legislation.
Public health guidelines stress that funerals can be held privately behind closed doors with family and close friends can be present and that there should be no public advertisement of funeral arrangements but death notices can be placed without arrangements.
Most churches have limited burials to 10 people plus a celebrant and urged people to follow social distancing guidelines. Most have said a celebration for the lives lost amid the coronavirus outbreak will be held after restrictions are lifted.
Chief Inspector Gary Reid said: “We have been made aware of comments and photographs posted online in relation to a funeral in the Turf Lodge area of west Belfast and are making enquiries.
“While we understand that the death of a loved one is a traumatic and sad time, and that a funeral is part of the grieving process, it is essential that people respect the current health legislation. I would urge all people to play their part to keep people safe during this global health emergency crisis."
Meanwhile, police are preparing a file for prosecutors after more than 200 people turned out in Co Tyrone to attend the funeral of former Sinn Fein councillor Francie McNally.
He served on Cookstown council between 1985 and 1989 and was buried in Ballinderry on Wednesday.
Those paying their respects as the funeral procession made its way to St Patrick's Church have been accused of putting lives at risk by failing to observe strict social distancing guidelines.
Two of Mr McNally's brothers were killed during the Troubles. Phelim McNally (28) was killed in a gun attack by loyalists at Francie McNally's home in 1988, while another brother Lawrence (39), an IRA member, was shot dead in Coagh in an SAS ambush in 1991.
Deputy First Minister Michelle O'Neill, who represents the area as a Sinn Fein MLA, said the rules apply to all.
"The rules are there for a reason. Everybody needs to follow them. Nobody is exempt," she said. "We're all being asked to do difficult things right now, but we're being asked to do them to save lives."
First Minister Arlene Foster said it was right that police had launched an investigation.
"Everybody needs to stick by the rules," she said. "Others who have lost loved ones will look at that and say well, we stuck to the rules even though it was incredibly difficult, even though we were in a lot of pain. It's right that it is investigated."
PSNI Chief Constable Simon Byrne said the police position was clear.
"People have had a lot of hurt and anxiety but it's no excuse to behave in a selfish way, to ignore guidelines that are really clearly available about limiting funerals to five family members," he said.
After officiating at the funeral, Father Peter Donnelly said 10 immediate family members were present at the burial.
"Church guidelines and the law of the land were observed and upheld," he said. "I had no prior knowledge or involvement with anything else that may have happened.
"I am concerned solely with the burial and that was conducted in line with the regulations that are current."
Mid-Ulster District Commander Superintendent Mike Baird said police had been assured that only family members would be in attendance.
"It is very disappointing to see some people blatantly ignored health advice and breached current legislation and, in doing so, they not only put themselves at risk but also put at risk close family members of the deceased and those officiating at the funeral," he said. "An investigation is under way, evidence is being gathered and a file is being prepared for submission to the Public Prosecution Service."
Mid-Ulster DUP MLA Keith Buchanan said there was nothing spontaneous about the gathering.
"There was an organised party of men accompanying the coffin alongside a relatively large gathering of other people," he said.
Local UUP Councillor Robert Colvin criticised the republican funeral as an insult to those working in the NHS.
"Regrettably these restrictions to ease the burden on our NHS staff were completely ignored," he said. "There is little point in Michelle O'Neill urging social distancing if republicans in her home county are going to assemble in large numbers in complete defiance of her advice."
TUV leader Jim Allister said considerable hurt would be caused to other grieving families.
Archbishop of Armagh and Primate of All Ireland Eamon Martin stressed that it is not the Church's responsibility to police funerals.
After speaking to Fr Donnelly, he said the family of the late Mr McNally and the funeral directors were all in agreement that the burial was being held for immediate family members only.
Archbishop Martin told BBC Talkback: "If a whole group of other people arrive on the scene, I don't think the priest who is in the middle of doing the funeral ceremony or the family who are bereaved can police these situations.
"Some people just don't abide by restrictions."
The funeral notice for Mr McNally announced that his remains would be leaving his family home for burial at St Patricks Church, Ballinderry, noting the date and time of the burial.