Sinn Fein's Martin McGuinness has unreservedly condemned the murder of former IRA prisoner Kevin McGuigan.
Mr McGuigan was the chief suspect in the murder of former Belfast IRA leader Gerard 'Jock' Davison.
There had been newspaper reports in recent weeks that some in the IRA wanted Davison's murder avenged.
Deputy First Minister Mr McGuinness said: "My thoughts are with the family of the man shot dead in the Short Strand tonight. I unreservedly condemn this appalling deed."
The MP for East Belfast, Gavin Robinson, said: "There can be no justification for the murder in Short Strand tonight. No one has the right to take the law into their own hands.
"Murder has no place in our society. Mr McGuigan clearly had a past, but if there was any connection between recent events, it should have been dealt with by the police - and no one else."
If the murder is linked to the IRA, it could lead to political fallout at Stormont, where the relationship between the DUP and Sinn Fein is already fraught.
But Mr Robinson said there was a need to establish the facts first. He added: "There should be no circumstances in which a police investigation should not be fully carried out, or in which 'internal housekeeping' is acceptable."
SDLP leader Dr Alasdair McDonnell condemned the murder.
"This was a brutal and terrible crime in Belfast and I utterly condemn those behind it. The perpetrator must be held to account for bringing this level of inhumanity and savagery back to our streets," he said. "In just two days a bomb has exploded near a children's playing field in Derry and a man has been murdered in east Belfast. We must stand against those who would seek to drag us all back to the ways of the past.
"I urge anyone with information about either of these actions to go to the police."
Sinn Fein councillor Niall O Donnghaile said: "I unreservedly condemn the shooting of a local man near his home in the Short Strand tonight and I am saddened to learn that the man has died. This action has shocked the local community and my thoughts are with the family.
"There can be no place for actions like this in our society. The community here rejects any attempt by any armed group to turn the clock back to the past."