Jordan Gray, 26, was shot dead in his own home in Shields Court, in the town of Motherwell, North Lanarkshire, on Sunday 14 December.
Sky News understands a shotgun was used in the murder.
Mr Gray’s body was discovered the following day, with Police Scotland having since gathered more than 1,200 hours of CCTV footage and conducted door-to-door enquiries in the hunt for the killer.
At a press conference on Tuesday, Mr Gray’s mother Lynn Gray and stepfather Michael Groome appealed for anyone with information to come forward.
Mr Groome said: “We are here today to appeal for any information leading to finding out who murdered our son in cold blood.
“The outpouring of love we have had since Jordan’s death is testament to the fact that he was a well-liked young man and, yet, someone stole him from us.
“We are devastated by our loss. His sisters and wee brother are struggling to understand how someone could do this to their big brother.
“Jordan’s baby will have to grow up without knowing how much his dad loved him.”
Mr Groome thanked the force for its continued support as he urged anyone with information to come forward.
He said: “Help us stop them from doing this to someone else and leaving another family heartbroken.”
Police Scotland did not allow questions to be asked during the press conference.
Detective Superintendent Grant Hendry, the senior investigating officer, said: “This is a really shocking crime, the murder of a young man in his own home.
“It’s vital we trace the person responsible and get answers for Jordan’s family.
“To date, we’ve gathered more than 1,200 hours of CCTV footage, conducted door-to-door enquiries, resulting in over 250 questionnaires being completed and issued 88 letters seeking further information.
“There’s also ongoing forensic analysis and other investigative opportunities in the background which aren’t visible to the public.
“Be reassured, we’re doing everything we can to trace whoever is responsible for Jordan’s death.”
Read more from Sky News:
Man who chased police officer with chainsaw jailed
Child serial killer Lucy Letby will face no further criminal charges
Investigating officers are keen to identify a person spotted in Shields Court around 10.30pm on 14 December, who was said to be wearing a dark jacket with the hood up and dark trousers.
DSI Hendry added: “If you know who this was, or think the description matches you, please come forward even if it’s just so we can eliminate you from our enquiries.
“It may be that information is known in the local area about who is responsible. No matter how insignificant you feel that information is, or if you think we’ll already know, please report it to us.”
Those with information can submit details directly to the inquiry team via an online portal. Anyone wishing to remain anonymous can contact Crimestoppers on 0800 555 111.
