The men eventually managed to negotiate their release, but as they drove away, the militants detonated a roadside bomb by remote control, killing all seven, Rasoolyar said.
It was unclear why the men were targeted, the spokesman said, adding that none of the seven worked for the authorities or were involved in any government activities. The Taliban often target Afghan civilians who work for the government or with foreign military or civilian organizations.
The volatile province of Zabul lies just north of Kandahar, a traditional Taliban stronghold which along with neighboring Helmand has been the focus of much of the fighting in recent months.
NATO bolstered its forces last year with more than 30,000 additional troops, mostly American, who have focused on cracking down on the Taliban in southern Afghanistan.
NATO said on Friday it had detained several suspected insurgents in the city of Kandahar a day earlier during an operation targeting Taliban leaders believed responsible for assassination attempts against Afghan government officials. The suspects were arrested during a search of a compound in the city, the alliance said in a statement.