President Hamid Karzai blamed the Taliban for the killings, which he described as brutal and cowardly. He said the laborers were "innocent people" going to the base to earn money so they could feed their families during the holy month of Ramadan. He added that their killers "will face the rage and anger of God and will be punished."
Provincial spokesman Din Mohammad Darwesh said there were four gunmen on motorcycles who pulled over the minivan.
"They just took them out of the car and shot them. They are all in their late teens and early 20's," Darwish said.
Both officials said it was unclear if the incident could have been in reprisal for a coalition airstrike that killed 18 Taliban fighters in another part of the province on Wednesday.
Logar, located just south of Kabul, has seen a sharp increase in insurgent activity this year. The Afghan army last week carried out a large operation against insurgents operating in the province.
The Taliban have said they will not stop fighting during Ramadan, which began last week, and will instead step up their attacks.
About 1,000 Afghan civilians have been killed and more than 2,000 wounded in the first half of the year, according to the United Nations. That marked a 24 percent increase in casualties compared to the same period last year.
As the NATO-led coalition last year started a withdrawal that will see most foreign troops gone by the end of 2014, the Taliban and other groups have unleashed a wave of bombings and assassinations around the country, testing the ability of Afghan security forces to respond with reduced help from international troops.
The Taliban have said they would go after government workers and anyone working for the U.S-led coalition as part of their campaign against Karzai's administration.
The Taliban have killed people working at the Logar base in the past. Last November, militants shot and killed two translators as they were heading to work on the base.
Last month, a Taliban suicide bomber struck outside of Afghanistan's Supreme Court, killing 17 people in the deadliest attack in Kabul in more than a year and a half. In April, insurgents assaulted a courthouse and government offices in western Farah province, killing 46 people, including two judges, six prosecutors, administration officers and cleaners working at the site.
Also in June, the U.N. special representative to Afghanistan, Jan Kubis, said insurgents were behind 74 percent of all civilians casualties in the first six months of 2013, and attributed the rise on the militants' "continuing disregard" for international laws on civilians in conflict.
Kubis also said that targeting government officials and civilians was a crime under international law. The Taliban have argued that government officials and workers are legitimate targets.
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Associated Press writer Patrick Quinn contributed to this report from Kabul.