It crashed into the vehicle park of a Lidl supermarket near Lisbon, killing the pilot and three French passengers, according to TVi24.
The plane is believed to have exploded in mid-air before crashing near the supermarket in a residential area. It had four people on board - one crew member and three passengers, when it crashed.
The Swiss-registered plane crashed shortly after a noon (1100 GMT) takeoff from Tires aerodrome, about 20 kilometers (12 miles) west of the Portuguese capital, Cruz said.
The twin-engine Piper PA-31 plane had just taken off on a flight to the southern French city of Marseille when it crashed, hitting a truck parked at the warehouse.
Officials described the weather at the time of the crash as clear skies with a light wind.
Thousands of evacuated Syrians stuck as transfer stalls
The British-based Syrian Observatory for Human Rights reported casualties, saying the explosion appeared to be caused by a bomb. Syrian state TV blamed the rebels for obstructing the deal, causing thousands of evacuees to be stuck in bus depots overnight.
A spokesman for the local emergency services, Andre Fernandes, said the plane was headed for Marseilles in France. Nearby houses were blackened by smoke, with nine people forced to move out of their homes. The cause is not known.
President Marcelo Rebelo de Sousa went to the site of the crash.
Authorities are yet to publicly identify those killed in the accident.
Tires is about 20km (12 miles) from Lisbon.The crash site is a auto park in a residential area between Lisbon and the upmarket resort of Cascais.Dozens of firefighters are at the scene.