PARIS, Dec. 13 (Xinhua) -- The death toll of the shooting attack near the Christmas market in Strasbourg, France has climbed to three on Thursday after a wounded victim succumbed due to his injuries, regional authorities said.

"The death toll, still provisional, is now set at three dead, five seriously wounded and eight minor injuries," Bas-Rhin prefecture was quoted as saying by local media.

One of the victims fighting for their lives was brain-dead, it added.

On Tuesday evening, an armed man opened fire against passers-by in the center of Strasbourg, which is close to German border, and stabbed others.

Witnesses told investigators that the suspect shouted "Allahu Akbar" (God is Greater) as he attacked people near the Christmas market, a target Paris Prosecutor Remy Heitz suggested may have been chosen for its religious symbolism.

"Given the targeted place, the attacker's operating way, his profile and testimonies collected from those who heard him shout "Allahu Akbar," the anti-terrorist section of the Paris prosecutor's office ... opens an inquiry into attempt of assassination linked to a terrorist enterprise," Heitz said.

The suspect is identified as Cherif Chekatt, 29. He has a criminal record and was known to intelligence services as "at risk for radicalization". He had been convicted 27 times in France, Germany and Switzerland for common law offenses, including armed robberies.

He exchanged fire with the anti-terrorism Sentinelle force that wounded him before he fled in a taxi. He fought a second time with police in the Neuhof district, according to Paris prosecutor.

Addressing lawmakers on Wednesday, Interior Minister Christophe Castaner said the Starsbourg-born fugitive did not cross the German border and was still at large in French territory.

A total of 720 police officers, supported by two helicopters, are involved in a huge manhunt for the attacker.

In an interview with CNews television, government spokesperson Benjamin Griveaux, on Thursday, said security forces were trying to catch Chekatt dead or live.

Asked if police had been instructed to catch the fugitive dead or alive, Griveaux said "It doesn't matter. The best thing would be to find him as quickly as possible..."

France raised its security threat level to highest, strengthening controls along its border with Germany, where agents from both countries stepped up checks of motorists' identity and vehicles crossing the Rhine river.

President Emmanuel Macron chaired an emergency security meeting on Wednesday after which he decided to deploy an additional 1,800 security forces to guarantee security in Christmas markets and ensure calm during the year-end holidays.