Kabul, Afghanistan (CNN) -- Afghan authorities on Tuesday raised the number of those killed by a suicide attack at a fuel depot near Kandahar International Airport to four people.
Eight people were also wounded in an attack carried out by three militants at a compound run by an international contractor called Supreme Group, according to a provincial government spokesman.
Zalmai Ayubi said all those killed and injured were Supreme Group security personnel. CNN cannot independently confirm that account.
The Taliban claimed responsibility for the attack.
Wearing vests packed with explosives, the militants stormed the compound Monday evening, Ayubi said.
One man drove a minibus toward the facility and detonated himself as he approached the main security gate, clearing the way for the other militants to enter the compound and engage in a firefight with security personnel, according to Ayubi.
The militants were later killed in a subsequent gun battle with police and security guards.
NATO, meanwhile, was not involved in the fight but had been monitoring the situation, as coalition forces encourage local and national forces to take on more prominent security roles throughout the country, said Maj. Jason Waggoner, a spokesman for the NATO-led International Security Assistance Force in Afghanistan.
The airport is located southeast of Kandahar City, long considered a hotbed of insurgent activity, and is used for both military and civilian fights.
A similar quick-strike tactic was employed by insurgents Sunday in the country's northeastern Parwan province, where six militants -- also wearing bomb-laden vests -- stormed the provincial governor's compound in an attack that left 25 people dead, including themselves.
The governor managed to escape that attack, which the Taliban later took responsibility for.
Suicide strikes -- along with roadside bomb attacks -- have become a hallmark of Taliban-style tactics.
CNN's Matiullah Mati contributed to this report