French police have issued a call for help to find the man suspected of opening fire near a Christmas market in Strasbourg.
Hundreds of police, soldiers and border agents on both sides of the Franco-German border are trying to find Chérif Chekatt, 29.
Two people died and 13 were injured in the gun attack in the eastern French city on Tuesday evening.
The gunman shouted "Allahu Akbar" ("God is greatest") as he opened fire.
Chérif Chekatt was already known to the French authorities as someone who had been radicalised into following an extreme form of Islam while in prison for crimes including robbery.
Police say anyone who sees the "dangerous" suspect should not approach him, but instead call an emergency hotline.
The lights of Paris' Eiffel Tower will be turned off at midnight in tribute to the victims, according to Mayor Anne Hidalgo.
How is the manhunt going?
France's Interior Minister Christophe Castaner told the parliament that more than 700 police officers and other members of the security forces were searching for the gunman, who was injured in an exchange of fire with soldiers who were patrolling the Christmas market in Strasbourg when the attack occurred.
Across the nearby border, German police are also conducting searches after France's Deputy Interior Minister, Laurent Nuñez, acknowledged that the gunman might no longer be in France.
Border agents are also checking vehicles crossing the Rhine river, which marks the Franco-German frontier, leading to long lines of traffic in both directions.
How did the attack unfold?
At about 20:00 local time (19:00 GMT) on Tuesday, a man opened fire close to Strasbourg's famed Christmas market near one of the central squares, Place Kléber, which attracts thousands of visitors.
France's anti-terror prosecutor Rémy Heitz said two people were killed and one was left brain-dead in the hail of bullets. Twelve other people were wounded, six of them seriously, he added.
The suspect was armed with a gun and a knife and escaped the area after commandeering a taxi, Mr Heitz said.
As he fled he came into contact with four soldiers, Mr Heitz said, and began firing at them. The soldiers fired back, apparently hitting him in the arm.
The attacker boasted to the taxi driver that he had killed 10 people, and also said he had been injured during a firefight with soldiers.
He ordered the taxi driver to drop him in the vicinity of the police station in the Neudorf area.