Afghan police have shot and killed five protesters in three separate incidents as riots broke out during demonstrations over this week's Koran burning incident.

Police said one protester was fatally shot and four people were wounded, including two police officers, when security forces and some protesters exchanged gunfire during a riot outside the police headquarters in the northern province of Baghlan. Another two protesters were killed and six were wounded in an exchange of gunfire during a protest in southern Uruzgan province.

Two more were killed in an exchange of gunfire during a riot outside an American base in eastern Afghanistan that also left two Nato troops wounded.

Governor Haji Mohammad Hassan said Nato and Afghan troops were firing in the air to disperse hundreds of protesters gathered in front of the base in Khogyani district in eastern Nangahar province. He said during the rioting, one man in an Afghan army uniform shot at Nato troops and seriously wounded two of them.

The fresh violence came one day after clashes between Afghan troops and protesters broke out in the capital and in three eastern provinces over the incident, leaving at least seven people dead and dozens wounded.

The US has apologised for the Koran burnings, which took place at a military base near Kabul, and said it was a mistake.

President Hamid Karzai said he shared the Afghan people's pain at hearing of the Koran desecration, but asked them to stay calm until an investigation is completed.

The unrest started on Tuesday when Afghan workers at the main American military base, Bagram Air Field, saw soldiers dumping books in a pit where garbage is burned and noticed Korans and other religious material among the rubbish.

The top US and Nato commander, General John Allen, quickly issued an apology and telephoned Mr Karzai to explain that a collection of religious materials, including Korans, had been mistakenly sent to be incinerated. As soon as someone realised what they were burning, they stopped and retrieved what was left, Gen Allen said.

Meanwhile, the Afghan president's office said it has received a letter from US president Barack Obama apologising for the burning of Korans. In the letter, Mr Obama expresses his "deep regret for the reported incident" and offers his "sincere apologies".