Police authorities nationwide have been advised to look out for the suspect after a number of house searches in Karlskrona failed to reveal his whereabouts.
The victim was the father of the suspect’s ex-girlfriend, Blekinge Läns Tidning reports.
The murder is reported to have taken place shortly before lunchtime when the older man intervened to prevent a fight between his daughter and the 20-year-old.
Police in Karlskrona also described the murder as a “relationship drama” but were reluctant to reveal any further details.
The suspect is a Karlskrona resident with a history of violent crime.