A massive air and ground search is under way for two missing US soldiers the Taliban claim to have captured after a battle with the insurgents in eastern Afghanistan.

The US military has offered a $20,000 reward for information leading to the safe release of the men, who are thought to have been seized in the province of Logar, south of Kabul.

The soldiers were tracked and ambushed in a shoot-out by Taliban fighters as they drove through the dangerous Charkh district in an armoured vehicle on Friday, according to Afghan district chief Samar Gul.

He said: "They stopped in the main bazaar of Charkh district. The Taliban saw them in the bazaar. They didn't touch them in the bazaar, but notified other Taliban that a four-wheel-drive vehicle was coming their way"

The second group of Taliban tried to stop the vehicle but opened fire when it did not halt, prompting its two occupants to shoot back, said Gul, who added that he believed one of the Americans may have been killed. A Nato official said he did not know if that was true. Another official, speaking on condition of anonymity, would not say whether the soldiers' trip was sanctioned or whether they had gone somewhere they were not supposed to.

"They didn't pay any attention to the police. Otherwise we could have kept them from going into an insecure area and now this unfortunate incident has happened," he said.

Local radio in Logar broadcast appeals from the US and Nato-led International Security Assistance Force (ISAF) for information about the two Americans .

"This morning two coalition personnel went missing. They are believed to have been captured by insurgents somewhere in Logar province," the broadcast said. "They may have been separated from one another or may be in the process of being moved."

Another US serviceman, Idaho National Guardsman Bowe Bergdahl, was captured in June last year by the Taliban, who have repeatedly issued videos of him denouncing the war.