He was stabbed to death at Divis Tower flats in west Belfast last night.
The victim was aged 62 and had lived in the tower block for a number of years and was well known in the area.
His body was discovered in a flat on the 14th floor on Sunday night.
He had been stabbed a number of times in the abdomen.
A 42-year-old man arrested on Sunday night remains in custody at the PACE suite at Musgrave PSNI station in Belfast.
Detective Supt Kevin Geddes of MIT has appealed for information.
“We are not in a position to confirm a cause of death until a post mortem examination has taken place but we are following a definite line of enquiry.
“Although we have a suspect in custody and residents in Divis Tower have been very helpful in providing information as part of our enquiries, we are still appealing for assistance.
“I would ask anyone who was on the 14th, 15th or 16th floors of Divis Tower and heard anything suspicious between the evening of Saturday 5 November and yesterday evening to contact detectives at Musgrave police station on the non-emergency number 101.
“Alternatively, if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”
West Belfast Sinn Féin MLA Fra McCann said he believed two floors of the flats were evacuated late on Sunday night while a forensic search was carried out.
Mr McCann added: “I know the man personally, he was a very kind and well-liked person.
“He was a very spiritual man, always had a good and kind word for people
“He lived in this tower block for many, many years and got on well with everyone in the tower.”
Detectives and CSI teams spent last night and today at the scene gathering forensic evidence to the murder inquiry.