On Thursday, scores of people paid their respects to the murdered man at his funeral.
They heard how Conor's parents said they would "rather bury their son" than hide those responsible for a murder as the priest conducting the funeral urged for people to assist the police in their investigation.
Fr Martin Magill said: "I ask you: “what have you done to your conscience to allow you to kill Conor? How can you sleep at night? If you have children, how can you look them in the eye, knowing what you were doing last Thursday night in this community?
"I would love you to have heard what Conor’s parents said as we prepared for this Requiem Mass: 'no parent brings a child into this world to take the life of another person'. 'We’d rather be burying our son today than hiding our son because he had killed someone else'.
"With those words in mind, let me add my support to the appeal by the PSNI for information which will lead to the detection and arrest of Conor’s killer and those who assisted it."
Fr Magill, delivering the homily at the Sacred Heart Church, said the community had demonstrated its strength in the support offered to the McKee family.
He said: "We don’t come to judge, instead we pray that God will forgive Conor his earthly faults and failings and bring him to the light and peace of heaven.
"As well as praying for Conor, we pray for his heartbroken family – sudden death at any time is traumatic but ever more so when Conor’s death was so brutally taken.
"Since last Thursday night, there has been a huge outpouring of support and care for you his family.
"Michelle’s home has had countless visitors over the course of the last week with people coming to offer sympathy, love and practical support.
"I had the opportunity to comment to Conor’s parents Tommy and Margaret how amazing the whole family has been during this horrendous ordeal; Tommy commented back to me: “we have been surrounded by such good people”.
"It is at such times that a strong community comes into its own."
Conor had been on bail for drugs offences prior to his brutal killing.
Fr Magill spoke of the loving father Conor was and how he loved relaxing with his family.
He continued: "Unfortunately, there were also the bad times from when he started to use drugs at an early age.
"Those early choices led him into shadows and darkness.
"In making those choices, he hurt himself, those closest to him and inevitably others suffered as well.
"He was, as his mother Margaret described him, a 'tortured soul'."
The priest added: "Conor struggled with addiction, he was offered help in various different ways and was soon to start a recovery programme.
"Some of his choices took him away from the potential he had.
"Personally speaking, having met with him on several occasions, I was fortunate to see glimpses of what Conor could be.
"Along with two others from a project established to set up a dedicated centre to assist young people recover from drug and alcohol addiction, I heard Conor talk about how he wanted to prevent young people making the mistakes he’d made and to help them break free from addiction."
Fr Magill said drugs wrecked lives and urged those with addiction problems to seek out help.
"Living a life in the shadows of drug addiction is not God’s plan for any of us," he said.
On Monday friends and family held a vigil for the 31-year-old and tributes of flowers and messages were left outside his home.
Neighbours and friends of the family spock of their shock of the death.
Detective Chief Inspector Justyn Galloway said: "We have had a very positive response from Conor's friends after our appeal last week.
"We also appealed to a person who phoned police in the early hours of last Friday morning with information about the murder to call back. That person has yet to do so."
He continued: "Conor was seen in the area of Rosapenna Street and Oldpark Road at 6pm last Thursday evening. We believe he was shot in his home at Glenpark Street at 6.15pm.
"I am appealing to anyone who saw Conor walking from the Oldpark area back to Glenpark Street between 6pm and 6.15pm, either on his own or with someone, to contact us."
Two men arrested over the murder on Friday were later released on police bail.