The attack, which occurred Friday on a road in southern Uruzgan province, was the deadliest yet in a wave of violence aimed at sabotaging the nation's first free vote, scheduled for September.
On Saturday, a bomb ripped through a bus carrying female election workers in the eastern city of Jalalabad, killing two of them and wounding 13 others. A spokesman for the Taliban claimed responsibility.
The assaults raised doubts over whether Afghanistan is ready to hold the vote and increased pressure on NATO leaders meeting in Turkey on Monday to deploy more peacekeepers here.
Rozi Khan, the Uruzgan police chief, told The Associated Press that assailants stopped the van on a road about 20 miles from the provincial capital, Tirin Kot.
The gunmen opened fire after they searched the documents of the 12 men inside and found that they had registered to vote. Two men escaped and alerted police, who found the 10 bodies but have made no arrests.
Khan said the men were traveling back from Tirin Kot to their homes in a district of the province also called Uruzgan.
Obaidullah Khan, the top political administrator in Uruzgan district, confirmed the attack but said 16 people had died, and just one man had survived.
It was impossible to immediately account for the discrepancy.
Obaidullah Khan said about six or seven attackers had launched the assault, while others hid in rocks nearby.
Taliban-led rebels have vowed to sabotage the polls but the Afghan government and the U.S. military are adamant they can go ahead as planned in September despite increasing security concerns.
Authorities were questioning the driver of the bus targeted in Saturday's bombing. The driver allegedly fled shortly before the blast.
"He is from Jalalabad, but we're not 100 percent sure he did this," said Faizan, the spokesman for the governor of Nangarhar province where the city is located. The spokesman, who uses only one name, declined to identify the suspect further.
Five badly injured passengers — including one child — were transferred for medical treatment to the main U.S. military base in Afghanistan at Bagram, north of Kabul, said Sayid Mohammed Azam, a spokesman for the Joint Electoral Management Body.
Others with less serious injuries were hospitalized in Jalalabad.
Azam said voter registration was continuing in Nangarhar province, despite some limitations imposed on the movements of female staff members after the attack.
A U.N. statement said those restrictions were in place while the security situation was assessed, but registration of women voters was continuing "wherever possible."
About one-third of the 4.5 million people registered to vote so far are women. Because of religious and cultural sensitivities in this deeply Islamic country, registration is segregated between the sexes.
The security threat has delayed registration in remote areas, and so far, only about half of eligible voters have signed up nationwide.