The 29-year-old gunman who killed three people at a Christmas market in Strasbourg before being shot dead by police after a two-day manhunt was a career criminal with convictions in France and several other European countries.

French police posted on their Police Nationale Twitter account, a call for witnesses for Strasbourg-born Cherif Chekatt, 29, the day after an attack on a Christmas market in Strasbourg. (French Police Nationale/via Reuters)

Cherif Chekatt had been convicted of crimes including violence and robbery and was added to a watchlist of possible extremists while in prison in France in 2015, by which point he was described by authorities as having become radicalised.

He had since been monitored by France's domestic intelligence agency, the DGSI, which monitors thousands of suspected extremists in France.

A photograph released by French authorities showed a man with dark, deep-set eyes, black hair, a short beard and a mark on his forehead.

One source said that a poster of Al Qaeda leader Osama bin Laden had been found in his cell in 2008.

Neighbours, however, described a man who was known in the area due to his criminal record, but kept a low profile, only venturing downstairs for a coffee and baguette.

"He wasn't totally into Islam," one neighbour named Zach, 22, told AFP, describing Chekatt as "discreet, not a thug", who lived alone in a small apartment in a dilapidated building in the same area as his parents.

"His family has lived around here for a while, but he lived on his own nearby," he said.

Chekatt had been sentenced 27 times - mostly in France, but also in Germany, Switzerland and Luxembourg, which are all easily reached from Strasbourg.

He was first sentenced at the age of 13 and was described by French Interior Minister Christophe Castaner as having exhibited criminal behaviour since the age of 10.

Described by one source as being aggressive at times, Chekatt was, however, said to be at the low end of the spectrum in terms of his radicalism, showing no hint of carrying out an attack.

In prison, the man who shouted "Allahu akbar" (God is greatest) during Tuesday's (Dec 11) attack was described as practising a radical form of Islam.

And although the propaganda wing of the Islamic State group claimed responsibility for Tuesday's attack and described Chekatt as "one of the soldiers of the Islamic State", the source said there was no sign he had any established links with Syria.

Chekatt was "a familiar composite portrait of today's jihadist", Anne Giudicelli, Director of the consulting firm Terrorisc, told AFP.

"He has ticked all the boxes of the profiles seen before."

At the nine-storey concrete block where Chekatt's name appeared on a letterbox, one local, Bemba N'diaye, 37, painted a grim picture of the area.

"People there are very isolated," N'diaye told AFP.

"It's a building for desperate people. No one wants to live there."

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More than 700 French security forces had been hunting for 29-year-old Cherif Chekatt since the bloodshed on Tuesday night.

He was believed to have been injured after exchanging fire with soldiers during the attack, but managed to escape and had not been seen since getting out of a taxi in the Neudorf area of the northern French city.

The gunman was one of the "soldiers" of the Islamic State militant group, its propaganda agency said on Thursday.

The perpetrator of "the attack in the city of Strasbourg ... is one of the soldiers of the Islamic State and carried out the operation in response to calls to target nationals of the coalition" against IS, the Amaq agency said in a message posted on Twitter.

Minutes before the fatal shooting on Thursday, a helicopter with powerful searchlight flew over Neudorf.

Interior Minister Christophe Castaner told reporters police swooped after the suspect was spotted in the street.

Officers tried to arrest him, but he shot at police. "They immediately returned fire and neutralised the assailant," Castaner said.

Dozens of police vehicles converged on the area where police were applauded after the shooting. "Bravo!" some shouted as people gathered at the police cordon, a source said.

Police in several other countries earlier joined the manhunt for Chekatt, a Strasbourg native and career criminal with at least 27 convictions in four European states.

Authorities published Chekatt's picture late Wednesday with police describing him as dangerous and urging people not to approach him.

A fifth person was detained by police for questioning on Thursday, in addition to the suspect's parents and two brothers who have been in custody since Wednesday.

The Strasbourg Christmas market is due to reopen on Friday.

French President Emmanuel Macron expressed "the solidarity of the whole country" towards the victims as he arrived for a European summit in Brussels on Thursday.

"It is not only France that has been hit ... but a great European city as well," he added, referring to the seat of the European parliament in the eastern French city that lies on the border with Germany.

Strasbourg's location in the heart of western Europe means that Germany, Switzerland, Belgium and Luxembourg can be easily reached by car or train, making the search for Chekatt more complicated.

Swiss police had reinforced border checks, while German authorities also widely published the photo of the suspect, which showed him with dark hair, a short beard and a visible mark on his forehead.

In 2016, a militant responsible for an attack on a Christmas market in Berlin was shot and killed only three days later in Milan in northern Italy after travelling through the Netherlands and France.

The Strasbourg suspect, who lived in a rundown apartment block a short drive from the city centre, was flagged by French security forces in 2015 as a possible Islamic extremist.

France has been hit by a wave of attacks from gunmen claiming allegiance to Al Qaeda or the Islamic State group since 2015, which have claimed the lives of 246 people before Tuesday's attack, according to an AFP toll.

No group has claimed responsibility for the Strasbourg attack, but social media accounts used by Islamic State sympathisers have celebrated the killings./.

VNF/AFP