Police said the man suspected of steering the truck had fled the crash scene and was later arrested.
Newspaper Die Welt said he had jumped out of the driver's cab and run down the street towards the Tiergarten, a vast park in central Berlin. It said several witnesses phoned police to inform them, including one who chased the suspect while on the phone, constantly updating officials on his whereabouts.
On Tuesday morning, investigators removed the black truck from the site for a forensic examination. People left flowers at the scene and notes, one of which read: "Keep on living, Berliners!" One woman was crying as she stopped by the flowers.
Berlin police are investigating leads that the truck had been stolen from a construction site in Poland. They said a Polish man was found dead inside the vehicle but added he was not in control of it.
German magazine Focus cited Karl-Heinz Schroeter, interior minister of the state of Brandenburg, as saying one of people found dead at the scene was shot, and that was probably the Pole.
Bild newspaper cited security sources as saying the suspect was named Naved B. and had arrived in Germany a year ago. In legal cases German officials routinely withhold the full name of suspects, using only an initial.
Local broadcaster rbb cited security sources as saying the man came to Germany via Passau, a city on the Austrian border, on Dec. 31, 2015.
Die Welt said police special forces stormed a hangar at Berlin's defunct Tempelhof airport at around 4 a.m. (0300 GMT). It said, without citing its sources, that the arrested man was registered there.
A refugee there who gave his name only as Ahmed told Reuters security guards had told him there was a raid at around 4 a.m.
Prosecutors declined to immediately comment on the report.
Stephan Mayer, a senior member of the Christian Social Union - the Bavarian sister party to Merkel's Christian Democrats, told broadcaster ZDF it was necessary to ensure that there were no copycat attacks.
Austrian Interior Minister Wolfgang Sobotka said on ORF radio he had told the heads of Austria's regional police forces to intensify surveillance measures.
He called for biometric and fingerprint checks to be introduced along the Balkan route travelled by many migrants arriving in Europe, in order to better control foreign jihadist fighters' movements.
London police said they were reviewing their plans for protecting public events over the festive period after the Berlin attack and the assassination of Russia's ambassador to Turkey on Monday.
Flags will be hung at half-mast around Germany on Tuesday and Berlin Christmas markets were closed for the day out of respect.
Dresden tourist information service said authorities had erected concrete blocks around the Striezelmarkt, one of Germany's oldest Christmas Markets, to increase security.
Christmas markets selling ornate, often hand-crafted decorations, seasonal foods and hot wine are a beloved tradition in Germany.
Manfred Weber, head of the center-right European People's Party, said: "It's not an attack on a country; it's an attack on our way of life, on the free society in which we are allowed to live."
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