23 February 2012 Last updated at 11:55 GMT
Many others were injured in the protests, while armed men also attacked at least two military installations.
Crowds shouting "death to Obama" have been throwing stones and setting fire to the US flag.
Meanwhile the Taliban has called on Afghans to kill and beat all Westerners in revenge for "insulting" the Koran.
In a statement a Taliban spokesman said Afghans should "not stop at protesting" but instead target military bases and personnel to "teach them a lesson that they will never again dare to insult the Holy Koran".
On Wednesday seven people were killed and dozens injured in protests over the burning of the copies.
President Hamid Karzai is meeting tribal leaders and politicians in an effort to find ways to calm tension.
Afghan security officials fear the protests could spread further, with pressure on people in other towns and cities to show their outrage at the desecration.
'Death to America'
Emergency talks are being held in Kabul to plan how to protect the capital.
He says Friday prayers may spark more tensions, depending on the tone set by religious leaders.
So far police and tribal elders have told the BBC there have been major protests in at least nine areas across the country, each involving many hundreds of people.
The worst incident was in Khogyani in Nangarhar province, where a man wearing an Afghan army uniform killed two Nato soldiers who are believed to be from the US.
Two protesters were also killed and seven injured as Nato forces opened fire when armed men attacked the US/Afghan base.
Further south, in Uruzgan province, two people were killed and at least eight others wounded, three of them police, in clashes between protesters and Afghan security forces, local officials told the BBC.
In northern Baghlan province one civilian was killed and two others injured, while two police were also hurt.
Another person was killed in Laghman province east of Kabul, where local police said several hundred people were chanting "Death to America".
More than 3,000 people gathered in Mehterlam, the capital of Laghman province, with some burning an effigy of President Barack Obama.
Afghan soldiers confiscated American flags during the protests in Kabul
Police say fights broke out as they stopped hundreds of protesters entering the centre of Kabul.
And in Asadabad, around 1,500 demonstrators were said to be burning US flags and tyres and shouting anti-American slogans.
A French military base to the east of Kabul was also attacked.
Earlier President Karzai said that "Afghan security forces should not use violence... and [should] protect civilian lives and property".
In a statement after an emergency debate, Afghan MPs condemned what had happened.
They also called for punishment of those responsible and asked the Afghan government to send its own delegation to Bagram to establish exactly what happened and why.
Isaf investigation
US Defence Secretary Leon Panetta said he and the top commander of US and Nato forces in Afghanistan, Gen John Allen, had apologised to the Afghan people "and disapprove of such conduct in the strongest possible terms".
Muslims consider the Koran the literal word of God and treat each book with deep reverence.
The Nato-led Isaf force is now investigating the incident, a spokesman told the BBC.
"It was the local workers who discovered the nature of the material and therefore stopped worse things from happening," said Brig Gen Carsten Jacobson.
Last year, at least 24 people died in protests across Afghanistan after a hardline US pastor burned a Koran in Florida.
Send your pictures and videos to yourpics@bbc.co.uk or text them to 61124 (UK) or +44 7624 800 100 (International). If you have a large file you can upload here.
Afghan police and plain-clothed security officials fire shots into a crowd of about 500 protesters in Kabul
At least another eight people have been killed, including two Nato soldiers, in violence across Afghanistan, after the burning of the Koran at a US base.
Many others were injured in the protests, while armed men also attacked at least two military installations.
Crowds shouting "death to Obama" have been throwing stones and setting fire to the US flag.
Meanwhile the Taliban has called on Afghans to kill and beat all Westerners in revenge for "insulting" the Koran.
In a statement a Taliban spokesman said Afghans should "not stop at protesting" but instead target military bases and personnel to "teach them a lesson that they will never again dare to insult the Holy Koran".
On Wednesday seven people were killed and dozens injured in protests over the burning of the copies.
President Hamid Karzai is meeting tribal leaders and politicians in an effort to find ways to calm tension.
Afghan security officials fear the protests could spread further, with pressure on people in other towns and cities to show their outrage at the desecration.
'Death to America'
Emergency talks are being held in Kabul to plan how to protect the capital.
Continue reading the main story
We went to the hospital where the injured were taken and a wounded policeman there told us that demonstrators shot at police. Officials say they are conducting an investigation to find out who opened fire.
After the violence, people escaped from the area, shops were closed and eventually demonstrators left. But it was an intense episode. People were shouting anti-American slogans expressing their outrage at the burning of the Koran. They also accused the Americans of being opposed to their religion.
At the scene
It started at about 09:00 when people from different villages around Baghlan converged on the town centre. About 1,000 demonstrators gathered in front of the police station and there was a lot of anger and violence. Then suddenly we heard an outbreak of machine-gun fire.We went to the hospital where the injured were taken and a wounded policeman there told us that demonstrators shot at police. Officials say they are conducting an investigation to find out who opened fire.
After the violence, people escaped from the area, shops were closed and eventually demonstrators left. But it was an intense episode. People were shouting anti-American slogans expressing their outrage at the burning of the Koran. They also accused the Americans of being opposed to their religion.
The BBC's Andrew North, in the Afghan capital, says many officials sympathise with the outrage the US has provoked across the country.
He says Friday prayers may spark more tensions, depending on the tone set by religious leaders.
So far police and tribal elders have told the BBC there have been major protests in at least nine areas across the country, each involving many hundreds of people.
The worst incident was in Khogyani in Nangarhar province, where a man wearing an Afghan army uniform killed two Nato soldiers who are believed to be from the US.
Two protesters were also killed and seven injured as Nato forces opened fire when armed men attacked the US/Afghan base.
Further south, in Uruzgan province, two people were killed and at least eight others wounded, three of them police, in clashes between protesters and Afghan security forces, local officials told the BBC.
In northern Baghlan province one civilian was killed and two others injured, while two police were also hurt.
Another person was killed in Laghman province east of Kabul, where local police said several hundred people were chanting "Death to America".
More than 3,000 people gathered in Mehterlam, the capital of Laghman province, with some burning an effigy of President Barack Obama.
Afghan soldiers confiscated American flags during the protests in Kabul Police say fights broke out as they stopped hundreds of protesters entering the centre of Kabul.
And in Asadabad, around 1,500 demonstrators were said to be burning US flags and tyres and shouting anti-American slogans.
A French military base to the east of Kabul was also attacked.
Earlier President Karzai said that "Afghan security forces should not use violence... and [should] protect civilian lives and property".
In a statement after an emergency debate, Afghan MPs condemned what had happened.
They also called for punishment of those responsible and asked the Afghan government to send its own delegation to Bagram to establish exactly what happened and why.
Isaf investigation
US Defence Secretary Leon Panetta said he and the top commander of US and Nato forces in Afghanistan, Gen John Allen, had apologised to the Afghan people "and disapprove of such conduct in the strongest possible terms".
Muslims consider the Koran the literal word of God and treat each book with deep reverence.
The Nato-led Isaf force is now investigating the incident, a spokesman told the BBC.
"It was the local workers who discovered the nature of the material and therefore stopped worse things from happening," said Brig Gen Carsten Jacobson.
Last year, at least 24 people died in protests across Afghanistan after a hardline US pastor burned a Koran in Florida.
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