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French troops stationed in the country's south-west have been told not to wear their uniforms when off base, reports say.

The order comes after two paratroopers were shot dead and a third injured as they used a cash machine in the south-western town of Montauban on Thursday.

Investigators are linking this to the killing of a paratrooper in Toulouse on Sunday.

France's defence minister has said no theories are being ruled out.

Asked if terrorism could be the motive, Gerard Longuet said: "Nothing permits us to rule out one theory or another."

France's elite airborne units are based in the south-west.

The dead paratroopers' regiment - though not the men themselves - recently served in Afghanistan, but French Foreign Minister Alain Juppe said there was "no kind of proof or indication" of a link.

The three men in Montauban were shot by a gunman on a scooter.

The 30-year-old soldier killed in Toulouse, 46km (29 miles) away, was shot by a gun of the same calibre. His attacker also used a scooter or motorcycle to escape.

The Toulouse prosecutor, Michel Valet, told reporters that it was possible that "the bullet fired in Toulouse and the bullets fired in Montauban came from one and the same weapon".

Two of Thursday's victims, aged 26 and 24, died on the spot while the third, 28, is in a critical condition.

Witnesses say one soldier tried to crawl away, but the helmeted attacker, in a black motorcycle outfit, turned him over and shot him again before escaping on the scooter.

All three victims were sappers with the 17th Parachute Engineer Regiment, based in Montauban, a picturesque town of 56,000 people in the Midi-Pyrenees region.

Le Figaro reports that anti-terrorist police are working on the assumption that the killer is a "lone wolf".

The newspaper says that Christian Lothion, the director of France's Judicial Police, has travelled to the region to take part in the investigation.

There are reports that all three of the dead soldiers were of North African origin, and that the injured man is black.

Montauban mayor Brigitte Bareges said the motive for the attack was a mystery.

"No-one understands. The regiment does not understand," she said.

"There's never a valid explanation for murder but we're dealing with a true killer."

Police said the soldiers had been withdrawing cash at around 14:10 (13:10 GMT) on Thursday when they were attacked, but theft did not appear to be the motive.

However, the Montauban attacker appears to have deliberately targeted soldiers, according to Pascal Paga, who owns a bakery near where the shooting occurred.

The gunman, he said, had pushed aside an elderly person waiting in line to use the cash-point before opening fire.

An army spokesperson told Agence France-Presse news agency that extra vigilance had been ordered, particularly at the entrances to barracks.

The orders on uniform affect service personnel at barracks in Toulouse, Montauban, Pamiers and Tarbes.