Police were called on Monday over concerns after a mother and her two children had not been seen for several days.
Officers forced entry into a property in Great Denham, where they found the bodies of a woman and two children, Bedfordshire Police said.
Police said they have identified a suspect, who was known to all three victims, and who they believe has since left the country.
Investigators fear the three alleged victims have been murdered.
Formal identification of the victims has not yet taken place, the force added.
Read more from Sky News:
‘Significant’ heat health alerts issued
Charlie Kirk’s widow faces his alleged killer in court
Assistant Chief Constable John Murphy called it an “incredibly complex investigation” and 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.”
He urged anyone with information about the incident to come forward.
ACC Murphy added: “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.”
