"He works in Berlin but comes home to Wiesbaden during the weekends", she said.
A shopping centre in the Prenzlauer Berg district of Berlin was closed in the afternoon due to a police operation.
Neighbouring flats are also being searched, according to German media.
The market at the centre of the atrocity reopened. Bild reported that he was alive until the attack took place.
Instead of producing papers, Amri drew a gun from his backpack and fired at one of two police officers, injuring him, Minniti said.
A reward of up to 100,000 euros ($104,000) had been offered for Amri's arrest. The alert warns he should be considered armed and unsafe. She had told Tunisian President Beji Caid Essebsi during a phone conversation that her government wanted to speed up deportation of failed asylum seekers and increase the number of those expelled, she added.
In a press conference on Friday, Italian interior minister, Marco Minniti said that "the man killed was without a shadow of doubt Anis Amri". A probe had been launched suspecting he was preparing "a serious act of violence against the state".More news: Total Team Effort Pushes Patriots Past Broncos, Clinch AFC East
German police said yesterday that they had arrested another IS suspect, a Moroccan named only as Redouane S, who was charged with being a member of the cell which carried out last year's deadly Paris attacks. The BBC said police have not commented.
After his arrival in Germany in July 2015, Amri's Isis sympathies meant German intelligence services classified him as a security threat, one of about 550 such people in the country.
"At first Tunisia disputed that this person was their state citizen".
"I ask him to turn himself in to the police".
"We can't rule out that the perpetrator is on the run", he said. "Those in Europe, kill the crusader pigs, each person to their own ability", he says in the video posted on Islamic State's Amaq news agency.
But he also called for greater cross-border police cooperation, suggesting some dismay that Europe's open border policy had enabled Amri to easily move around despite being Europe's No. 1 fugitive.