Jean-Philippe Ksiazek, AFP | Yellow vest protestors occupy a traffic circle on December 11. More protests are planned for Saturday, but the government is urging protestors to stay home in the wake of the Strasbourg attack.

The French government on Thursday urged "yellow vest" protesters not to hold another round of demonstrations this weekend as police hunted for a second day for the fugitive gunman who attacked a Christmas market in the eastern city of Strasbourg.

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Government spokesman Benjamin Griveaux called on the anti-government protesters to be "reasonable", citing the strain on security forces after the attack in Strasbourg on Tuesday evening.

Police across several European countries have launched a manhunt for the main suspect, a 29-year-old Strasbourg native, who killed two and injured 13 after opening fire on shoppers.

The suspected killer, identified as Cherif Chekatt, is thought to have been injured after exchanging fire with soldiers, but managed to escape and has not been seen since.

"Our security forces have been deployed extensively these past few weeks," Griveaux told CNews television.

"It would be better if everyone could go about their business calmly on Saturday, before the year-end celebrations with their families, instead of demonstrating and putting our security forces to work once again," he added.

>> Strasbourg shooting: tourists and locals among the victims

So-called "yellow vest" protesters, known for their fluorescent high-visibility jackets, had called for a fifth round of protests this Saturday against President Emmanuel Macron.

The protests began on November 17 over fuel tax increases, but snowballed into a revolt over living standards as well as Macron's perceived indifference to the problems of ordinary citizens.

The appeal came as authorities announced that a sixth person had died since the start of the protests, after a 23-year-old was hit by a truck in southern France near Avignon.

Even before Tuesday's attack in Strasbourg, the government had scrapped a fuel tax increase slated for January, a core demand of the protesters, who mainly live in rural areas and smaller towns and rely heavily on their cars.

Macron also announced a hike in the minium wage, tax relief on overtime work and a rollback on taxes for many pensioners in a televised address to the nation on Monday night.

>> 'All smoke and mirrors': Yellow Vest protesters reject 'crumbs' offered by Macron

Last Saturday nearly 90,000 police were mobilised across the country for the protests, with 8,000 officers and a dozen armoured vehicles deployed in the capital, where scores of stores, museums and monuments were closed.

While some of the movement's representatives have said they are open to halting the protests to negotiate with the government, others have said Macron's concessions are not enough.

Wide search

Hundreds of police in France are now hunting for Chekatt, whose picture was published late on Wednesday in a bid to track a career criminal who has at least 27 convictions in four European countries.

His mother and father, as well as two brothers, were detained for questioning Wednesday.

Strasbourg's location at the crossroads of France, Germany, Switzerland, Belgium and Luxembourg, makes the search more complicated.

Chekatt, 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 while in prison.

Strasbourg suspect: a violent criminal on France's terror watchlist

Prime Minister Edouard Philippe announced Wednesday that France's anti-terror Sentinelle operation, which counts around 7,000 soldiers nationwide, would be boosted by a total of 1,800 troops over the coming days.

Among the casualties in Strasbourg, two were killed outright and another has been declared brain-dead, while 12 more were injured, six critically, France's anti-terror prosecutor Remy Heitz said.

They included one Thai tourist who was among the dead.

Thai Prime Minister Prayut Chan-o-cha sent a letter of condolence to his French counterpart saying he was "profoundly shocked and saddened to learn of the horrendous attack in Strasbourg".

The statement said the Thai citizen had been on holiday in the city.

In Rome, the foreign ministry said one of the injured was an Italian journalist covering the European parliament, but did not confirm media reports that he was in a serious condition.

According to a tweet by Poland's embassy in Paris, a Polish citizen was also among the injured.

(AFP)

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