French President Nicolas Sarkozy warned Monday that weakness in the face of terrorism would be "a grave error," after a failed bid to rescue French hostages in Africa whose kidnapping was blamed on Al-Qaeda.

Sarkozy made the comments at the White House, where he met with President Barack Obama who offered condolences over the deaths of the two French hostages captured in Niger.

French officials said the two men were killed "in cold blood" by their captors during a French rescue attempt after they were chased across the border into Mali by Niger forces on Saturday.

"The United States and France are determined to be allies on the subject of terrorism," Sarkozy said. "We believe that weakness is a grave error and we have no choice but to fight these terrorists wherever they are."

"Democracies cannot yield, democracies must defend themselves when such fundamental values are at stake," he added.

A Malian security source told AFP that irrefutable proof of the involvement of Al-Qaeda in the Islamic Maghreb (AQIM) had been found at the site where French special forces backed by helicopters attacked the kidnappers.

The two Frenchmen were snatched at gunpoint from a Niamey restaurant late Friday before horrified onlookers. The bodies of childhood friends Antoine de Leocour and Vincent Delory, both aged 25, were found in the desert after the botched rescue operation.

Obama said the kidnapping, one of several blamed on AQIM, "points to the challenge of terrorism that we jointly share, and this is just one more area in which cooperation between France and the United States is so critical."

Sarkozy thanked the US president for his "expression of solidarity with the tragedy that France has just experienced, with these two young Frenchmen cowardly murdered by barbarians, by terrorists," said Sarkozy.

The French and US leaders' focused mainly on France's current leadership of the G20 and G8 economic groupings.