Attacks in two different Afghan provinces - Nangarhar in the east and Kunduz in the north - have left several people dead, including many of the assailants.
In Saturday's first attack, a pre-dawn Taliban raid was thwarted by soldiers at a US military facility - Forward Operating Base Fenty - that is part of the Jalalabad airfield.
An Isaf statement said that no Afghan National Army (ANA) troops or Isaf soldiers were killed in the incident.
Eight attackers were killed, many of whom had been wearing ANA uniforms, Ahmad Zia Abdulzoi, a Nangarhar government spokesman, said.
Zabiullah Mujahid, a Taliban spokesman, said there were 14 attackers and that 11 of them were killed, but the claim could not be independently corroborated.
The day's second attack involved a motorcycle bomb that killed at least 10 people, including two policemen, according to the Afghan interior ministry.
A bomb hidden in a motorbike exploded on a busy street in Kunduz's Imam Sahib district, killing seven civilians.
The bomb was detonated just as a vehicle belonging to a police official drove past. The official - Commander Mohammad Manan - was killed along with one of his bodyguards and five civilians, Abdul Qayum Ebrahimi, Imam Sahib's police chief, said.
Ebrahimi said they believed the bombers had targeted Manan.
The Taliban claimed responsibility for a previous attack on the Jalalabad airbase in June, which involved a car bomb and rocket attack on 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.
Al Jazeera's Sue Turton, reporting from Kabul, said the Jalalabad base had been targeted before and was a key site for transporting military supplies from Kabul.
Saturday's attacks followed a failed suicide bombing of a convoy of Afghan and Nato-led troops on Friday in the outskirts of Kabul, signalling a possible surge in violence in the lead-up to two important international events regarding the conflict in Afghanistan.
Nato leaders gather in Lisbon next week, with Afghanistan to top the agenda as European members reassess their commitments amid flagging support for the war back home.
Barack Obama, the US president, will also review his Afghanistan war strategy next month and has committed to starting a gradual troop withdrawal of US troops from July 2011.
Violence is at its worst across Afghanistan since the Taliban were overthrown in 2001, with civilian and military casualties at record levels - despite the presence of 150,000 foreign troops.
Saturday marked the ninth anniversary of the fall of the Taliban to US-backed Afghan forces.