The Taliban launched a pre-dawn attack on a NATO base in eastern Afghanistan on Saturday, triggering a firefight with foreign and Afghan forces that left eight militants dead.
Another 10 people, including three children, were killed in a motorcycle bombing in a market in a remote area of northern Afghanistan in an attack apparently targeting a local pro-government militia leader.
The Taliban, which often exaggerates details of its attacks and foreign casualties, said 14 suicide bombers were involved in the strike on the base at Jalalabad airport, which was the target of a similar attack in June.
But the International Security Assistance Force (ISAF) said only one was wearing a suicide vest. It said eight militants were killed.
"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.
NATO said no foreign troops or Afghan soldiers were injured in the attack on one of the country's largest military bases.
Hours later, 10 people, including three children, were killed and 18 others were wounded when a motorcycle packed with explosives detonated in a market in the remote Imam Saheb district of northern Kunduz province.
Afghanistan's interior ministry condemned the attack as "un-Islamic and inhumane" and said an investigation had been launched.
District chief Mohammad Ayoub Haqyar told AFP that the explosion bore the hallmark of previous Taliban attacks 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.
A third attack on Saturday, also a motorcycle bomb, wounded five people, including a child, in the southern city of Kandahar, a security official and a local hospital doctor said.
The explosion happened in the Aino area of the city, a newly-built neighbourhood partially owned by President Hamid Karzai's brother, Mahmood, who is the head of the provincial assembly.
The hardline Islamist Taliban held 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 a bloody campaign to regain power and drive out tens of thousands of foreign troops in Afghanistan to protect Hamid Karzai's Western-backed government.
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.