The Tunisian Interior Ministry said that the "terrorist cell" was "active" between Fouchana, south of Tunis, and Oueslatia, the hometown of Amri's family in central Tunisia.
Amri's nephew said he had been in contact with his uncle through telegram, it said.
Security for the long Christmas weekend was heightened throughout Italy and at the Vatican on Saturday following the killing by police of the man believed to be responsible for the Berlin market truck attack.
"After an investigation, it was found that the person that was killed is, without any shadow of a doubt, Anis Amri, the presumed suspect in the Berlin lorry attack", said Marco Minniti.
Meanwhile, Spain's interior minister Juan Ignacio Zoido announced that intelligence services in the country are investigating a possible internet communication between Amri and a Spanish resident on 19 December.
As his partner lay wounded on the ground, Scata returned fire and killed Amri after hitting him with two shots. After fleeing from Germany and through France, he was shot dead by Italian police in Milan on Friday. He was killed after he pulled a gun and shot an Italian officer in the shoulder during a routine police check.
Angela Merkel has sought to quash fears that Germany is no longer capable of protecting its own people by promising to crush terrorism and increase the number of deportations of risky extremists following the Berlin terror attack. After Amri's death, the group released a video showing him pledging allegiance.
Amri, 24, who had spent time in prison in Italy, was stopped during a patrol in Milan's Sesto San Giovanni suburb.
They had been trying to deport him after his asylum application was rejected in July but were unable to do so because he lacked valid identity papers and Tunisia initially denied he was a citizen.