Three bodies were found after police forced their way into a house.
A mother and two children who had not been seen for several days are feared to have been murdered, police said.
They were found after officers forced their way into a house in Carnoustie Drive, Great Denham, near Bedford on Monday, according to Bedfordshire Police.
A suspect has been identified but is thought to have fled the country.
Assistant Chief Constable John Murphy said: “This is a deeply distressing incident in which a mother and her two children are believed to have been murdered.
“Our thoughts are first and foremost with all those affected.
“We recognise that this will cause concern in the local community and beyond.
“This is the early stages of what is an incredibly complex investigation.
“We are committing all necessary resources to establish exactly what has happened and to find the person responsible.
“As a result of inquiries undertaken so far, we have identified a suspect, who was known to all three victims, and who we believe has since left the country.
“While there is nothing to suggest there is any wider risk to the public, we will be increasing the police presence in and around the area to support the investigation and provide reassurance to residents.”
He asked for anyone with information or who saw anything suspicious in Carnoustie Drive on Friday or Saturday to come forward.
Formal identification of the victims has not yet taken place.
