Bashary said the situation had now been brought under control, but could not say whether the security guards had managed to escape and whether they had managed to seize the prisoner they were after.
Hamid Karzai, the Afghan president, has demanded that US coalition forces hand over the security guards involved in the shootout.
The president called for the "immediate handover by the coalition forces to the Afghan government of the private security guards involved in the killing of Kandahar province security officials", the statement said.
"President Karzai said that such incidents negatively impact the state-building process in Afghanistan and called upon coalition forces to avoid actions that weaken the government," it said.
David Chatar, Al Jazeera's correspondent reporting from the Afghan capital, Kabul, said that the US-led coalition had released a statement saying no coalition forces were present at the time of the gunfight.
The statement said that the guards were contractors for a private security firm loosely affiliated with coalition forces, our correspondent said.
"So everybody is denying any contact with these people," Chater said.
"But the point is there have been many questions raised before about the coalition forces, and particularly the Americans, using these security firms and using these Afghans - some of them with criminal records - to work with them for security," he said.
Kandahar in southern Afghanistan is a Taliban stronghold.
Fears of mounting violence have grown ahead of key presidential and provincial council elections in the country in August.
Chater said Monday's shooting does nothing to help Karzai in the run-up to the election.
"As far as the president is concerned, this is a big blow to the government here," he said.
"It undermines his attempts to keep his government going and we're right in the middle of an election campaign."