Bedfordshire Police discovered the bodies of a woman and two children in Great Denham on Tuesday (July 7).
A triple murder investigation has since been launched and the force confirmed it had identified a suspect who fled the country.
Detectives have since released an image of Ndodana Mkhanyisi Tshuma, 45, who also goes by the name of Mark, from Bedford.
He is wanted in connection with the deaths and is believed to have left the country from Heathrow Airport on a British passport on Saturday (July 4).
He is a British citizen of Zimbabwean heritage.
Although formal identification has yet to take place, police believe the victims to be his wife Nothabo Zandile Tshuma, 42, known as Zandile, and his daughters Natalie, 15, and Nala, 5.
Detective Inspector Lee Martin, senior investigating officer, said: “We have been carrying out numerous lines of enquiry as part of this fast-paced, complex investigation.
“We know that Mark Tshuma left the country on Saturday and is now believed to be in Zimbabwe.
“We are urgently working to find and apprehend him, and would appeal to him directly to hand himself in.
“Mark, unthinkable harm has been caused to those around you, and this has left your relatives and friends utterly devastated.”
He added: “Criminal investigation knows no borders. We are actively working with national and international agencies to pursue every available line of enquiry to track you down.
“Please do the right thing, come forward and hand yourself in to local authorities.
“Our thoughts are still very much with Zandile, Natalie and Nala, as well as all of those who loved and knew them, at this extremely difficult time.”
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