Eight militant fighters were killed in a firefight with foreign and Afghan forces stationed at Jalalabad airport in eastern Afghanistan, which is one of the largest military bases in the country, the alliance said.
The Taliban, which often exaggerates details of its attacks and foreign casualties, said 14 suicide bombers were involved but the International Security Assistance Force (ISAF) said only one was wearing a suicide vest.
No foreign troops or Afghan soldiers were injured in the attack, it added.
"The forward operating base received small arms fire from an unknown number of insurgents and after gaining positive identification of insurgent fighting positions an ANA and ISAF quick reaction force was sent to the area," it said.
Hours later, eight people -- two police and six civilians -- were killed and 18 others were wounded when a motorcycle packed with explosives detonated in a market in the remote Imam Saheb district of the northern province of Kunduz.
District chief Mohammad Ayoub Haqyar told AFP that the explosion was similar to previous attacks by the Taliban but there was no immediate confirmation of responsibility.
A pro-government militia commander was among the dead and was the likely target, he added.
"It's too early to say what the target was but we believe Commander Abdul Manan could have been the target. He was killed," said Haqyar, adding that an investigation was under way.
The hardline Islamist Taliban were in power in Afghanistan from 1996 until 2001, when they were ousted in a US-led invasion after the September 11 attacks in the United States.
They have since mounted an increasingly bloody campaign to regain power and drive out tens of thousands of foreign troops now based in Afghanistan to protect the Western-backed government of President Hamid Karzai.
Militant fighters have been increasing attacks over the last nine years and 2010 is currently the deadliest for the 150,000-strong international force, with more than 630 foreign soldiers killed.
The Taliban has been widely using improvised explosive devices, which are responsible for the bulk of the military deaths as well as scores of civilian casualties.
The insurgents claimed responsibility for another brazen daylight attack on the Jalalabad air base in June, in which a car bomb was set off and rockets were fired at foreign forces.
A number of assailants were killed and two service personnel were injured during the attack, which came just days before US General David Petraeus took up his post as NATO's top commander in Afghanistan.
Jalalabad has more than 2,500 military and civilian personnel and is one of NATO's largest bases in Afghanistan after Kandahar in the south and Bagram, north of Kabul.
Kandahar and Bagram have also been targets for Taliban attacks in the past.
Saturday's attacks came after a failed suicide attack in the Afghan capital Kabul on Friday, which was aimed at a convoy of foreign and local troops near a military base.
ISAF said separately on Saturday that it had detained a "senior Taliban leader" and several other suspected militants after discovering a significant weapons cache in the southern province of Helmand.
Several armed insurgents were killed in an air strike targeting a senior Taliban leader in northern Baghlan province, while Afghanistan's interior ministry said they had uncovered a haul of homemade bombs in Kunduz province.
All the operations happened on Friday.
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