Detectives from the Surrey and Sussex Major Crime Team are asking for information on the whereabouts of Viktoras Bruzas.
Officers say they are investigating a double murder in at a house in Fetcham and Mr Bruzas was now thought to be in the Sussex area.
Surrey Police say they were called at around 12.30am this morning (Thursday November 27) after another resident at the property on The Copse found a man and a woman with serious injuries, believed to be stab wounds.
Officers arrived at the address a short time later and the victims, in their 50s were pronounced dead at the scene.
Mr Bruzas, 38, from Walton-on-Thames, is believed to be driving a black Mercedes registration AU11 WJY and is likely to now be in the Sussex area but also has connections to Surrey and South East London.
Senior Investigating Officer Detective Chief Inspector Mark Preston, said: “This is a tragic incident where two people have lost their lives and our thoughts are with their family at this extremely difficult time.
“We are still in the very early stages of the investigation but we need to trace Viktoras Bruzas as a matter of urgency. I would urge members of the public not to approach him but to call Surrey Police immediately if they know his whereabouts.
“A large number of officers from Surrey and Sussex are working on locating Mr Bruzas.
“Sometimes, for whatever reason, people may wish to provide information anonymously and this can be done so through the independent charity Crimestoppers on 0800 555 111.
“Fetcham is a small, close-knit community and this incident is likely to have a lasting impact on the village but we will have specialist and neighbourhood officers in the area working with residents while they come to terms with these tragic events. I ask that the privacy of those closely affected by this incident is respected at this time.”
A man in his 30s has been arrested in connection with the incident on suspicion of conspiracy to commit murder at a property in Walton-on-Thames.
Information can be passed to Surrey Police on 101 or 999 in an emergency.