The Paris prosecutor's office said today that a fourth person had died from their wounds following Tuesday's Strasbourg Christmas market shooting.

"The person had been fighting for their life," an official in the prosecutor's office said.

The gunman, Cherif Chekatt, was killed on Thursday night after firing on police, ending a two-day manhunt that involved more than 700 members of the security forces.

Earlier today, the city's popular Christmas market was reopened, a day after French police shot dead the gunman who carried out the attack - which has been claimed by the so-called Islamic State group.

Cherif Chekatt was killed late yesterday when a police patrol spotted him on a street in the district where he was last seen after Tuesday night's attack on Christmas shoppers.

But France's interior minister has dismissed the claim that the gunman was one of the "soldiers" of the Islamic State group, as investigators sought to understand his motives.

The lights on the market's towering Christmas tree were lit up today for the first time since the attack.

"I hope life will get back to normal but I'm not too sure," said Franck Hoffmann as he opened his wooden chalet offering Christmas candles and ornaments today.

"Business isn't going to be what it was," he said.

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Questions remained over how Chekatt was able to evade the tight security perimeter set up for an event long known to be a prime target for jihadist groups.

Around 500 police, security agents and soldiers are controlling access at checkpoints on the bridges leading to the river island, a UN World Heritage site, that houses the market.

The goal is to "create a bubble with searches at the entry points," Mayor Roland Ries said after the attack, while regional government representative Jean-Luc Marx said he had not determined "any flaws in the security measures".

Many residents, however, were not convinced after Chekatt managed to slip through the controls with a handgun and a knife.

"It doesn't surprise me," said Emeline, 38, who works in the city centre. "You wear a heavy coat, put something in the bottom of your bag. You can bring in what you want."

France's anti-terror prosecutor Remy Heitz is to hold a press conference in Strasbourg today while Interior Minister Christophe Castaner attended the reopening of the market, which usually draws two million people every year.

France has been on high alert since the start of a wave of jihadist attacks in 2015, which prompted a threefold surge in the security budget for the market, to €1m.

Chekatt, a 29-year-old career criminal 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.

The propaganda wing of the Islamic State group claimed responsibility for Tuesday's attack, calling Chekatt one of its "soldiers".

Strasbourg's deputy mayor Alain Fontanel admitted that despite patrols, plainclothes police, profilers and video surveillance, "the risks can be reduced, but not eliminated".

"We can't pat down and search everyone, only carry out random checks," he said, adding that huge lines at checkpoints would only create a new potential target for terrorists.

"Someone who wants to get in an area this big with a weapon can do it," he said.

Such reasoning was little comfort to the residents and tourists who flock to the Strasbourg market.