Ndodana Mkhanyisi Tshuma is believed to have fled the UK after the discovery of the bodies in Great Denham on Monday.
The 45-year-old, who goes by the name Mark, is from Bedford and is a British citizen of Zimbabwean heritage.
He’s thought to have flown from Heathrow to Zimbabwe on Saturday.
The three victims are believed to be his wife Nothabo Zandile Tshuma, 42, known as Zandile; and his daughters Natalie, 15, and Nala, 5 – had not been seen for several days.
Bedfordshire Police found the bodies when they forced entry to the house.
Detective Inspector Lee Martin appealed to the suspect 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 said.
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“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.”
Anyone with information is asked to urgently contact the force on 101, or go via Crimestoppers on 0800 555111 to stay anonymous.
