No Afghan or foreign soldiers reportedly died in the clashes.
Separately, four Taliban fighters were killed and four others seized in Zabul in the southeast, during joint military operations led by Afghan and multinational forces, Faridullah Khan, the province's security chief, said.
But Al Jazeera's correspondent in Afghanistan said the Taliban has denied knowledge of these operations.
However, he said clashes took place overnight in various places between Kabul and Kandahar.
The Taliban is particularly active in the southern and eastern areas of Afghanistan.
The latest fighting comes after international forces acknowledged the loss of three soldiers in two separate bombings on Friday.
Two more Nato soldiers were killed the same day when a roadside bomb blew up their vehicle while they were on a security patrol on a busy road west of Kandahar city.
Another Western soldier was killed in a similar incident elsewhere in the south, the Nato-led force said on Friday, without giving the exact location of the incident.
The nationalities of the soldiers have not yet been released.
With the latest casualties, 32 troops out of the nearly 70,000 mostly Western soldiers stationed in Afghanistan have died since the start of the year.
US officials say they expect pledges of extra forces and equipment at a Nato summit in Bucharest early next month.
British media has reported that Nicolas Sarkozy, the French president, plans to send an extra 1,000 French soldiers to Afghanistan.
The spike in violence concides with a video message to TV networks from a Taliban commander who has been hiding for seven years.
Jalaluddin Haqqani, head of the Taliban in southeastern Afghanistan, vowed a renewed campaign in Afghanistan against US and Nato "invaders".
"The Americans said the Taliban was beaten and defeated but we are not defeated," he says in the video.
"We will defeat [George] Bush [the US president] and continue our jihad until doomsday."