People have been told not to approach 58-year-old Kieran McLaughlin who is described as being 5ft 7in tall, of medium build, with blue eyes and grey hair. He is believed to have been wearing dark coloured clothing.
A Police Service of Northern Ireland spokesman (PSNI) said: "The public are requested not to approach this person, but are asked to contact police immediately."
Police are also appealing to Mr McLaughlin to contact detectives immediately.
Barry McCrory, 35, was gunned down in a flat in Londonderry city centre yesterday morning less than 24 hours after father-of-four Kevin Kearney, 46, was found dumped in a lake in north Belfast. He had also been shot.
Both victims were known to police for previous offending.
Police have yet to officially attribute blame but the finger of suspicion has been pointed firmly at dissident republican extremists opposed to the peace process and who have carried out gun attacks as a way of administering their own brutal form of vigilante justice.
Mr McCrory was murdered in front of his partner in the Shipquay Street area at about 11am yesterday. A man carrying a rucksack burst into his first floor apartment and shot him.
Derry is the current UK City of Culture and, even though it is a major base for dissident republicans, it has been largely free of any major terrorist incidents since January.
Both murders took place ahead of a visit to Northern Ireland by Prime Minister David Cameron, who flies in today for a major investment conference.