Police also dispatched a bomb squad to the scene to check whether there were explosives in the van, the senior security official said.
The horrific crash comes on the one year anniversary of the Stockholm terror attack in which a hijacked lorry killed five people and seriously injured a dozen more.
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A security source said he was probably German. Please avoid the area.
German Chancellor Angela Merkel promised a full investigation after a man killed three people by driving a van into a street cafe in the western city of Muenster, then fatally shot himself on the scene.
Amri was shot dead by Italian police in Milan four days later after travelling through several European countries. Hours later, police spokeswoman Vanessa Arlt said "we didn't find anything (to those reports) but we're still investigating in all directions and not excluding anything".
Police have urged people in Muenster to stay inside their homes and avoid the crash scene in the city's historic downtown.
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The vehicle plowed into people sitting at tables outside the Grosser Kiepenkerl restaurant, which is popular with tourists.
"At the moment, there is no evidence that there is any Islamist background" to the attack, said Herbert Reul, the interior minister of North-Rhine Westphalia, the state where Münster is located.
The attack comes after a terrorist ploughed into a Berlin Christmas market in December 2016, killing 21 people. "Our contemplations are with the casualties and their friends and family", she said.
Although authorities are in no way confirming this rumor, many believe that it is not a coincidence this attack fell on the exact one-year anniversary of an nearly identical incident in Stockholm, Sweden in 2017.
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Anxious neighbors formed search teams in effort to find 35-year-old Timothy Jerrell Cunningham who was last seen February 12th. Police previously called his disappearance unusual but said there had been no indications of attack on Cunningham.