A vehicle belonging to the family has been found 13 miles east of the District of Columbia in the state of Maryland, the outlet cites DC Police Chief Cathy Lanier as saying.
"Evidence collection will go on for several days. There's still a lot more we don't know," the Post quoted Lanier as saying at Friday's press conference.
The family's neighbor told the outlet he witnessed smoke coming out of the Savopoulos' $4.5-million mansion on Thursday afternoon. When firefighters gained access to the house and pulled out the victims, three of them had blunt-force injuries.
Lanier did not elaborate on the possible motives behind the crime.
Savopoulos was the chief executive of American Iron Works, the country's leading manufacturer of building works.
The Savopoulos family is survived by two of the couple's daughters, Abigail and Katerina Savopoulos, whose friends told the Post they were at their boarding schools at the time of the incident.