Germany's chancellor has said she will “greatly strengthen” security in the country after the Berlin Christmas market attack in which 12 people died.

The main suspect in the attack - Anis Amri was shot dead by police in Milan in the early hours of this morning.

Earlier this week, German officials admitted that Amri had been under surveillance for several months this year prior to the attack.

Authorities started investigating the 24-year-old in March this year after a tip-off he might be planning a robbery to raise money to buy automatic weapons for a possible attack.

They followed him until September, when it was decided there was no evidence to back up the original suspicions.

During that time, Amri was involved in a bar fight as well as drug dealing in a park, according to the covert operation.

The Tunisian had been denied asylum in Germany but his deportation was stalled.

German chancellor Angela Merkel also said she has spoken to the Tunisian President and told him deportations of failed asylum seekers need to be sped up:

“I spoke to my counterpart in Tunisia and we have intensified our collaboration to combat terrorism,” she said.

“Those who have no right to reside in Germany will see the consequences. We will accelerate measures to increase the numbers of people deported who don’t have the right to live in Germany.”

Meanwhile a “top German security official” told Sky News that Amri was linked to a network recruiting extremists for Islamic State.

He appears to have posted a video online, declaring his desire to avenge Muslims killed in air strikes.

Islamic State's Amaq propaganda wing released the footage of the 24-year-old's declaration of support for leader Abu Bakr al Baghdadi just hours after Amri was confirmed dead.

It is not clear if the video was taken before or after the attack.

Italian interior minister Marco Minniti said Amri had been identified "without a shadow of a doubt."

Mr Minniti did not release further details of the operation, citing an ongoing investigation.

A European-wide manhunt was launched for Amri after Monday's attack, but Milan police said they had no intelligence he was in the city.

He had arrived there just hours earlier on a train from France.

Local media said Amri shouted "Allahu Akbar" ("God is Great"), during the firefight.

"We had no intelligence that he could be in Milan," police chief Antonio De Iesu said.  

"They had no perception that it could be him otherwise they would have been much more cautious."

He was identified by his fingerprints.