NATO's International Security Assistance Force (ISAF) was unable to confirm reports that a US-run base in Khost province had come under attack but said it was investigating the reports.
"From what I understand it is still ongoing, we are getting details," a spokeswoman told AFP.
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Local police chief Adbul Hakim Is'haqzai told AFP that Taliban militants had first attacked Forward Operating Base (FOB) Salerno before retreating to occupy a secondary school in Khost city, the provincial capital.
The school was near a smaller US-run base, FOB Chapman, he said.
Seven CIA agents were killed in a Taliban attack on FOB Chapman in December, in what was the worst attack on US intelligence officials since 1983, when the US embassy in Beirut was bombed.
The Saturday attack began when insurgents launched rockets and gunfire on Salerno in the early hours of the morning, Is'haqzai said.
He told AFP at 5:30am (0100 GMT): "Now the fighting (at Salerno) has slowed down," but there was an ongoing exchange of fire between militants and security forces at the school.
Residents reported hearing gunfire.
"There are gunshots being heard all around my home. I'm scared of the attackers entering my home and of being bombarded by coalition forces," said resident Amir Shah, whose home is near the Gharghast High School in Khost.
Taliban spokesman Zabihullah Mujahed contacted AFP to say the insurgent group had despatched suicide bombers to the base.
"Twenty-eight Taliban suicide bombers have launched an attack on a coalition base in Khost," he said from an undisclosed location.
"They have entered the base," he said.
The Talban are known to exaggerate their claims.
FOB Salerno was visited on August 19 by the commander of international forces in Afghanistan, US General David Petraeus, where he met the 3rd Brigade Combat Team of the 101st Airborne Division, which he formerly commanded, ISAF's website says.
Petraeus told them: "You are all in a tough neighbourhood and in a very challenging environment. You are faced with extreme terrain, tough weather and tough enemies.
"The insurgents you face most in this area are very tough fighters, they are experienced, generally pretty well-equipped and they know the neighbourhood," he said, adding they had made "real progress in protecting the population".
Petraeus commands almost 150,000 US and NATO soldiers in Afghanistan, fighting a vicious Taliban-led insurgency that is hottest in the south and east of the country.
Khost borders Pakistan, source of fighters, funds and fertiliser to make the ubiquitous IEDs the Taliban deploy along with suicide bombers and targeted assassinations in the war, which is nearing its tenth year.
