The local intelligence head was also killed and the governor was critically injured.
He said the governor, Zalmay Wesa, was wounded and taken to the hospital.
In a statement, the Foreign Office Spokesman in Islamabad Dr Mohammad Faisal said that Pakistan strongly condemns the Kandahar attack.
Col. Peters says the attack appears to be Afghan-on-Afghan, noting the assailant was killed.
General Scott Miller, who took command of U.S. and North Atlantic Treaty Organisation forces in Afghanistan a month ago, had left the meeting moments earlier.
Afghanistan's head of state, President Ashraf Ghanii, initially lost in the national election that took place in 2014 before he was given the title.
Miller was present during the shooting but uninjured. "Responding to the shooting, Pentagon spokesman Lieutenant Colonel Kone Faulkner told Reuters that the attack will not change the U.S. resolve in its South Asia strategy if anything it made them more resolute".
Australia Could be the Next Country to Move Its Embassy to Jerusalem
Israeli Prime Minister Benjamin Netanyahu said he had recently spoken to Morrison and welcomed the Australian policy shift. At the same time, it must be noted that the new Australian government is not about to recognize Palestinian statehood.
Three senior Afghan officials were reported to be among the casualties, but there were conflicting accounts on whether they were killed or wounded.
However, at least two Afghan security officials were killed, including the region's police chief and intelligence chief.
The officials had reportedly met to discuss Saturday's parliamentary elections that are due to be held countrywide.
Khalid Pashtun, a member of parliament from the province, said Afghan Security Forces cordoned off the area and a USA military helicopter circled overhead as a gun battle that began at 3 p.m. local time raged on for more than one hour.
He was accused of abuses, including torturing Taliban inmates, but had brought reasonable security in Kandahar, the birthplace of the Taliban militants.
Poll-related violence has increased ahead of the long-delayed vote, with hundreds of people killed or wounded in attacks across the country.
The Taliban claimed responsibility for the attack in Bagram, which is the home of a sprawling USA military base.
The attack comes ahead of parliamentary elections Saturday, which the Taliban has threatened to disrupt.
On Wednesday, an Afghan Parliament member, Abdul Jabar Qahraman, who was seeking re-election, was killed in a Taliban bomb blast in neighboring Helmand province.
Gen. Scott Miller, the commander of USA and North Atlantic Treaty Organisation troops in Afghanistan, who was present at Thursday's meeting, was unhurt in the incident.