Commander Amanda Peterseim, another spokeswoman for the Nato forces, later said that all of the "approximately four" attackers were killed in
"They either detonated themselves or were killed," she said.
James Bays, Al Jazeera's correspondent in Afghanistan, said it "seemed to be a complex attack by the Taliban".
"The information we are getting is that there was a suicide attack at one of the base's entrances" followed by an hour of fighting with small arms, he said.
Officials said six fighters were involved in the attack.
Witnesses inside the base also reported hearing what sounded like rocket explosions.
The Kandahar governor's office said that one foreign soldier had been wounded by the reported rocket fire.
The air base had come under attack even the past. Taliban fighters attempted storm the air base on May 22, just a few days after they attacked Bagram Air Field, the main US base in the country.
Around 30,000 international troops are deployed in the southern regions of Helmand and Kandahar.
It has been repeatedly said that US and Nato forces are planning a major operation in Kandahar but so far they resisted the kind of push they launched in Helmand.
Elsewhere, six Afghan private security guards were beheaded during a bank robbery in the northern city fof Mazar-e-Sharif.
Sherjan Durani, a police spokesman in Balkh province, said on Tuesday that an unknown number of robbers killed the guards and stole about $269,000 in US and Afghan currency.