Berlin police said on Tuesday that investigators assume the driver of a truck that plowed into a crowd at a Berlin Christmas market, killing 12 people and injuring 48 others, did so intentionally in a suspected terrorist attack.

The truck crashed into people gathered around wooden huts serving mulled wine and sausages at the foot of the Kaiser Wilhelm memorial church, which was left as a ruin after World War Two, in the heart of former West Berlin on Monday evening.

"Our investigators assume that the truck was deliberately steered into the crowd at the Christmas market at Breitscheidplatz," police said on Twitter.

"All police measures related to the suspected terrorist attack at Breitscheidplatz are progressing at full steam and with the necessary diligence," police said.

The incident evoked memories of an attack in Nice, France in July when a Tunisian-born man drove a 19-tonne truck along the beach front, mowing down people who had gathered to watch the fireworks on Bastille Day, killing 86 people. That attack was claimed by Islamic State.

Interior Minister Thomas de Maiziere had previously said there were indications that the incident in Berlin was an attack.

Police said that the man found dead in the truck was a Polish citizen but added he was not in control of the vehicle. The nationality of the suspected driver, who fled the crash scene and was later arrested, was unclear, they said.

German media cited local security sources as saying that there was evidence suggesting the arrested suspect was from Afghanistan or Pakistan and had entered Germany in February as a refugee.

Local broadcaster rbb cited security sources as saying the arrested truck driver came to Germany via Passau, a city on the Austrian border, on December 31, 2015. It cited the sources as saying the man was born on January 1, 1993 in Pakistan and was already known to police for minor offences.

If that is confirmed, it could further worsen sentiment toward migrants in Germany, where more than a million people fleeing conflict and poverty in the Middle East, Africa and elsewhere have arrived this year and last.

The record influx has hit Chancellor Angela Merkel's popularity ratings and boosted support for the anti-immigrant Alternative for Germany (AfD). Senior AfD member Marcus Pretzell blamed Merkel for the attack on Twitter.

Austrian Interior Minister Wolfgang Sobotka said on ORF radio on Tuesday that he had told the heads of Austria's regional police forces to intensify surveillance measures, although there was no concrete evidence that an incident was about to happen.

Sobotka also called for biometric and fingerprint checks to be introduced along the Balkan route to better control foreign jihadist fighters' movements.

Berlin police are investigating leads that the truck had been stolen from a construction site in Poland. They have taken the truck for a forensic examination.