Politicians in Berlin are calling for a city-centre ban on “tank-like” 4x4s after a driver reportedly lost control of his car and hit a group of pedestrians in the German capital, killing four people.

Police have opened an involuntary manslaughter investigation into the 42-year driver of a Porsche Macan who reportedly overtook cars waiting at a traffic light in the central Mitte area at 7.10 pm on Friday, before mounting the pavement on the other side of the road.

A 64-year-old woman, her three-year-old grandson, a Briton and a Spanish national, both in their 20s, died at the scene. Police said the family of the 29-year-old Briton, who was living in Berlin, had been informed.

The exact circumstances of the accident, which took place on Invalidenstrasse, a road lined with restaurants and shops with a 30km/h (19mph) speed limit, were unclear. There has been speculation the driver, who is being treated in hospital for head wounds, may have experienced medical problems. Citing police sources, newspaper Tagesspiegel reported on Monday the man may have had an epileptic seizure.

A 67-year-old woman and a six-year-old child were also travelling in the Porsche Macan.

A spontaneous vigil was held on Saturday night for those who died, amid a wider debate about the threat to pedestrians and cyclists posed by ever wider and heavier vehicles on urban streets.

Stephan von Dassel, the district mayor of Berlin-Mitte, said “armour-like” 4x4s did not belong in the city, as every driving error put the lives of people at risk. “These [cars] are also climate killers. They are a threat even without an accident,” he said.

Oliver Krischer, a deputy leader of the Green party in the German parliament, called for size restrictions on 4x4s allowed into city centres. “The best solution would be a nationwide rule that allowed local authorities to set size limits,” Krischer told Der Tagesspiegel newspaper.

While the German government is committed to what it calls the Verkehrswende, the green transformation of its transport sector, the number of 4x4s registered on German roads has surged in recent years.

Last month, 4x4s, or SUVs, became the most popular newly registered car type in Germany for the first time, with a market share of 22.2%. More than 1m sports utility vehicles are expected to be registered in Germany by the end of the year, with the average driver aged between 46 and 65.