More than 1,000 Afghan protesters threw stones at police Wednesday and security forces fired shots in the air in a second day of violent clashes after copies of the Koran, Islam's most holy book, were burned at a major NATO airbase.

Protesters shouted Death to America! and Death to (President Hamid) Karzai in a large demonstration on the outskirts of the Afghan capital Kabul, while a second rally was underway in another area of the city, Reuters witnesses said.

Separate protests were also underway in the Jalalabad in the east where demonstrators praised the leader of the Afghan Taliban, screaming Long live Mullah Omar!, Reuters witnesses said.

Afghan media said demonstrations had also begun in the western city of Herat, which is usually one of the more stable parts of the conflict-wracked country.

In Kabul, protesters charged at police lines and smashed car windows while police fired back with water cannons in a bid to disperse the angry crowd who were blocking a major road.

The U.S. government and the commander of NATO-led forces in Afghanistan apologised Tuesday after local labourers found charred copies of the Koran as they collected rubbish at the sprawling Bagram Airbase, prompting demonstrations by as many as 2,000 people.

U.S. Defence Secretary Leon Panetta issued an apology for inappropriate treatment of Islam's holy book at the base to try to contain fury over the incident - a public relations disaster for Washington as it tries to pacify the country ahead of the withdrawal of foreign troops in 2014.

Protests raged for three days across Afghanistan in April last year after a U.S. pastor burned a Koran in Florida.

(Reporting by Mirwais Harooni, Writing by Rob Taylor, Editing by Amie Ferris-Rotman)