The victim was shot in the republican Creggan area of Londonderry shortly after 1.00am and died soon afterwards in hospital.
A local politician said the rumour on the streets was that the man was mistaken for someone else by the killers.
A priest who went to the scene said it appeared that the victim, understood to be 22, was chased and shot by a group of masked men, possibly while delivering pizza in the area.
The Police Service of Northern Ireland area commander, Chief Inspector Chris Yates, said: "This was a cold-blooded shooting."
It was two hours before police attended the scene because of fears of an ambush.
Mr Yates insisted they had responded to the shooting within 10 minutes, knew the victim had been taken to hospital and that witnesses were at the hospital.
"The initial call was that masked men were lying in wait in the area, so under those circumstances and with the terrorist incident we have seen most recently in Fermanagh where two police officers were nearly killed, we were not going to go blindly rushing into an area until we were satisfied it was safe to do so," he said.
Foyle SDLP Assembly member Pat Ramsey said strong rumours in area were that the murdered man was a victim of mistaken identity.
"The word on the ground is that it was mistaken identity. Taxi drivers in the city have a great reputation for getting it right and one said to me 'They got the wrong fella'."
The victim, he said, was a 22-year-old man from the Bogside area, close to the Creggan.
"He lived only a stone's throw from where he died."
Mr Ramsey said he had spoken to the victim's father and the family was devastated.
"We all thought there was an end to the Troubles. For anyone, the worst nightmare is someone coming to the front door and saying your son has been shot dead.
"The family don't know of any circumstance at all why their son would be taken out and shot. The father actually said to me 'That bullet was meant for someone else'."
The Foyle MLA accused dissident republicans of being responsible.
"The only people who have access to weaponry and guns of this nature are dissident republicans, the only people who have been on the war path in recent times are dissident republicans.
"There has been an increase in dissident republican paramilitary shootings and beatings in recent weeks - we have a gang who are emulating what the Provisional IRA did in the '70s and '80s with their kangaroo courts."
He said people in the area did not want the violence and those responsible needed to be marginalised by the community.
Dissident republicans recently issued threats against drugs dealers in Londonderry and some 20 people had been told to get out of the city.
But he said there was no suggestion the victim of the shooting had been involved in anything or had any history of past involvement.
Sinn Fein Assembly member Martina Anderson said nothing could justify what had happened and called on the organisation responsible to disband.
She said: "This was a criminal act and anyone who attempts to attach any kind of political justification to it is deluding themselves and our community."
The Foyle MLA added: "We are in a new era, we are creating a new society for the younger generation and there can be no place for this type of activity."
Parish priest Father Stephen McLaughlin, who was called to the scene by police at around 3.30am, said the whole community would be shocked by what had happened.
He said: "This is quite brutal, quite horrific. The details I have is that a young man was pursued by a group, a few people possibly masked, who shot him dead in a grassy area on the approach to the Creggan.
"There was some mention that perhaps he had been delivering pizza."
He added: "When I heard the news I just felt sick - you are being taken back to a place you thought you had left behind.
"It is going to be a nightmare for this young man's immediate family and the local community will be shocked."
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