BERLIN - On a drab, graffiti-sprayed square on the outskirts of Milan, two Italian police officers, one of them a trainee, spotted a suspicious young man with a backpack. It was 3:15 a.m. Friday. A thief? Possibly. They pulled him aside for an identity check.

The officers did not know that the man had already fled hundreds of miles across the heart of Europe, evading an international dragnet. They confronted the 24-year-old, who, using street-slang Italian picked up in Sicilian jails, insisted that he was a traveler from Italy's deep south.

They told him to empty his backpack. Instead, Italian officials say, he pulled a gun.

Anis Amri, a self-proclaimed soldier of the Islamic State, rapidly shot one officer in the shoulder before ducking behind a car.

"Poliziotti bastardi!" - police bastards! - Amri shouted.

The second patrolman, trainee Luca Scatà, fired back, killing the suspect.

The shoot-out ended the violent arc of Amri's life, marking another salvo in a relentless new wave of Islamist terrorism in Europe that has vexed the ability of nations to thwart it. German authorities say they believe the Tunisian national is the same man who hijacked a truck with a payload of steel Monday, shot its Polish driver, and rammed it into a Berlin Christmas market.

"He was the most-wanted man in Europe," said Italian Interior Minister Marco Minniti.

The market attack has sparked an outcry for sweeping reforms and bolstered security while raising serious questions about German police and intelligence lapses as well as Europe's handling of criminal migrants. As a result, in a country that cherishes personal privacy, new laws are being pushed in Germany that could ramp up surveillance and extend judicial powers.

Chancellor Angela Merkel thanked Italian authorities Friday while adding that "the Amri case raises a number of questions. . . . We will now press ahead and look into how far state measures need to be changed."

Hours after the shoot-out, Islamic State's Amaq news agency released a video of Amri that was tauntingly filmed only 1.5 miles from the German Chancellery in Berlin. He seemed calm, yet certain, in a black-hooded windbreaker on an iron bridge as he called on Muslims in Europe to rise up and strike at "crusaders."

"God willing, we will slaughter you like pigs," he said in the video, whose date and location were not given but looked as if it was filmed under wintry skies. He added: "To my brothers everywhere, fight for the sake of Allah. Protect our religion. Everyone can do this in their own way. People who can fight should fight, even in Europe."

The authenticity of the video could not be independently confirmed, but previous material released by Amaq has been credible. Earlier, a statement carried on Amaq described Amri as inspired by the Islamic State.

In Oueslatia, Amri's bleak home town in Tunisia, news of his death had reached his mother, five sisters, and three brothers, who until the end held hopes that the German authorities were after the wrong guy.

His brother Walid Amri, 30, sounded distressed and was struggling to speak over the phone. Women were wailing in the background. "This is a very difficult time for the entire family," he said, before his voice broke.

While Anis Amri's death ended the hunt for the person who drove a truck into a teeming Christmas market on Monday, killing 12 and wounding dozens, it also suggested the security risks inherent to Europe's open borders as well as flaws with its deportation and migrant systems.