The Berlin suspect has been shot dead in Milan, Italian security sources say - as Danish police reported a possible sighting.
Anis Amri, a 24-year-old Tunisian, has eluded capture since the attack on Monday that killed 12 people and injured another 48.
Danish police said a man matching his description was seen in Aalborg, about 450 miles north of the German capital.
Police in the North Jutland region said the man was between 20 and 30 years of age, with a black beard, and was wearing a black knitted hat and glasses, and carrying a black shoulder bag.
Police urged people to stay away from the area as officers have an ongoing operation there.
Authorities in Germany and elsewhere have been hunting for Amri, who is believed to be the driver of the truck that rammed through the crowd of shoppers at the market.
On Thursday, police in Denmark searched a Sweden-bound ferry in the port of Grenaa after receiving tips that someone resembling Amri had been seen there. But police said they found nothing indicating his presence.
It comes after footage emerged showing Amri at a Berlin mosque just hours after the attack.
The video, published by German public broadcaster RBB, was taken by police officers on a regular stake-out at the mosque, but Amri was not a suspect at that time.
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