Earlier reports said all three had died. Police said the soldiers were withdrawing cash, but theft did not appear to be the motive. The attacker, wearing a helmet with a visor, sped off after opening fire, BBC reports.

The attack took place near a military base housing the country's 17th Parachute Engineer Regiment. Some 15 spent cartridges were found at the scene, police said.

"The theft was not the motive of the murders," a police official in Montauban told the BBC, adding that all avenues of inquiry were currently open.

He described a potential link between Thursday's shootings and the gunning down of another soldier in Toulouse on Sunday as "a possibility, not a certainty".

The two soldiers who died were aged 24 and 26 and the third, aged 28, is in hospital. French media reports quoting officials earlier said that the third soldier had died from his injuries, but the defence ministry and police later said he remained in a critical condition.

France's Defence Minister, Gerard Longuet, issued a statement expressing his "deepest sorrow at the assassination of the two soldiers, and the wounding of a third". He said he had every confidence that the police would ensure justice was achieved in the case.

A large number of police officers are already involved in an extensive search for the gunman and prosecutors have said that they are considering a number of possibilities, including that the shooting was the result of a personal dispute.

The incident follows another shooting, on Sunday, when a 30-year-old soldier was shot dead by an assailant on a motorcycle in a residential area of Toulouse, 29 miles (46km) south of Montauban. The south-west of the country is home to all of France's elite airborne units.