Isaf did not specify the nationality of the missing soldiers, but US officials told the Associated Press news agency (AP) that they are American.
The governor of the province told Al Jazeera that he believes the missing Americans work for a Provincial Reconstruction Team, a military-led development team.
Samer Gul, the administrative head of Charkh district in Logar, blamed the Taliban for the disappearances. He said the Taliban had noticed the soldiers when their vehicle passed through a market.
"They stopped in the main bazaar of Charkh district. The Taliban saw them in the bazaar," Gul said. "They didn't touch them in the bazaar, but notified other Taliban that a four-wheel vehicle was coming their way." He says the men were then ambushed.
There have been unconfirmed reports that the Taliban have offered to hand over the body of the dead American in exchange for the release of prisoners.
Al Jazeera's James Bays, reporting from the capital, Kabul, said the US has offered a $20,000 reward for information about the missing men.
"Military vehicles are reading out messages through loud speakers to the local people, offering a reward of $20,000 for any information on the whereabouts of the two men," he said.
"What is puzzling though is why two US servicemen would set out from Kabul and then end up in southern Logar province, over an hour's drive.
"Normally you'd expect military personnel who are making that journey either to make it in an armoured convoy or to travel by air by a helicopter."
Logar is southeast of Kabul, the Afghan capital, in an area that has seen growing insurgent activity over the last few years.
Captures of foreign soldiers are rare in Afghanistan. The only other soldier known to have been captured is Bowe Bergdahl, an American who was captured by the Taliban in Paktika province in June 2009. Paktika is near Logar in eastern Afghanistan.
His fate and whereabouts remain unclear, though he appeared in a video released by the Taliban in April.