Berlin (AFP) - Tunisia on Saturday said it had arrested the nephew of Anis Amri, the suspected Berlin truck attacker gunned down by Italian police, as Germany searched for the jihadist's possible accomplices.

Tunisia's interior ministry said the nephew and two other suspects, aged between 18 and 27, were detained on Friday and were members of a "terrorist cell" connected to Tunisian-born Amri.

It made no direct link between the trio and the Berlin assault on Monday, when Amri is believed to have hijacked a truck and used it to mow down people at a Christmas market, killing 12.

The 24-year-old went on the run and was the focus of a four-day manhunt before being shot dead by police in Milan after opening fire first.

The Berlin rampage was claimed by the Islamic State group, which released a video on Friday in which Amri is shown pledging allegiance to IS chief Abu Bakr al-Baghdadi.

The Tunisian interior ministry said in a statement that Amri had sent money to his nephew so he could join him in Germany, and had allegedly urged him "to pledge allegiance to Daesh (IS)".

The unnamed nephew also claimed his uncle was the leader of a jihadist group based in Germany, known as the Abu al-Walaa brigade, it added.

The arrests come as German authorities probe whether Amri had help before or after the attack. Hundreds of investigators are set to work on the case throughout the holiday season.

"It is very important for us to determine whether there was a network of accomplices... in the preparation or the execution of the attack, or the flight of the suspect," federal prosecutor Peter Frank said Friday.

- Criticism -

Seven of those killed were German nationals, a federal police spokeswoman told AFP. The other five victims came from the Czech Republic, Italy, Israel, Poland and Ukraine.

The fact Amri was able to travel to Italy unhindered despite a Europe-wide arrest warrant has raised uncomfortable questions for intelligence agencies.

German security services have also faced criticism for not keeping better tabs on Amri before the Berlin carnage, even though he was a known criminal.

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Interior Minister Thomas de Maiziere denied there had been a blanket security failure.

It "is impossible to monitor every person suspected of posing a threat around the clock," he told the newspaper Bild am Sonntag.

Chancellor Angela Merkel pledged a "comprehensive" analysis of how Amri was able to slip the net, vowing to speed up the deportation of rejected asylum seekers such as him.

Amri was killed after firing at two officers who stopped him for a routine identity check on Friday near Milan's Sesto San Giovanni railway station.

Amri had a few hundred euros on him but no telephone, Milan police said, adding that he had arrived in Italy from France.

A French source close to the investigation said train tickets found on Amri suggested he had travelled from the southern French city of Lyon to Chambery in the southeast.

From Chambery he boarded a train to Milan via Turin, the source said, adding that Amri paid for at least one ticket in cash.

- Christmas 'not ruined' -

Amri left Tunisia for Italy in 2011. He spent four years in prison there for starting a fire in a refugee centre, during which time he was apparently radicalised.

After his release he headed to Germany in 2015, taking advantage of Europe's Schengen system of open borders -- as he did on his return to Italy this week.

German security agencies began monitoring Amri in March, suspecting he was planning break-ins to raise cash for automatic weapons to carry out an attack.

But surveillance was stopped in September because Amri was seen primarily as a small-time drug dealer.

Meanwhile, as Germany celebrated Christmas Eve, locals and tourists in Berlin visited the scene of the truck assault, and many lit a candle or left flowers in memory of victims.

"It's really nice there are so many people here and it's still open," said Marianne Weile, 56, from Copenhagen.

"Even though you are really sad about what happened you can still keep Christmas. It's not like this crazy guy ruined it for everybody."