The light aircraft is believed to have exploded in mid-air before crashing near the supermarket warehouse shortly after midday.
El Mundo also reports that a Portuguese person unloading a truck in the carpark died when the plane crashed.
The plane came down near the Lidl Supermarket in Tires near the coastal town of Cascais 20 miles west of Lisbon. Four people were slightly injured, emergency services said.
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Madrid travel north on the back of their 2-1 win away over Bayern Munich in the Champions League and with their morale sky high. I think we deserved the victory because we had many chances to score more goals. "We need everyone and everyone responds".
The Tires airfield said the plane was a twin-engine Piper PA-31 Navajo aircraft and was Swiss-registered. There were more than 50 rescue workers at the site.
The spot where the plane crashed is just 150 metres from a local school.
One nearby house was also blackened by smoke, and nine people had to be evacuated from their homes.
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About three dozen firefighting vehicles rushed to the scene, arriving within six minutes, according to officials.
"There are four dead, the pilot and his three passengers", a spokesman for Portugal's Office of Prevention and Investigation of Aeronautical Accidents told AFP, saying further details about the incident and the fatalities were not immediately known.
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