Afghan officials said nine people died on Friday, seven of them in the relatively peaceful western province of Herat, where the assault was made on the consulate in the capital.
The Koran burning has inflamed anti-Western sentiment already smouldering over abuses by US-led foreign troops, such as the release last month of a video showing US Marines urinating on the corpses of dead Afghans.
President Hamid Karzai's government and the US-led NATO mission in Afghanistan had appealed for calm and restraint, fearful that Taliban insurgents are trying to exploit the anti-American backlash.
But in Herat city, three people died as protesters surged towards the US consulate while four more were killed elsewhere in the province, provincial spokesman Moheedin Noori told AFP.
"Seven people were killed and 50 others were injured -- mostly in gunfire -- across Herat province," said Noori.
Another protester was shot dead and two were wounded when demonstrators tried to overrun the Czech-led military-civilian provincial reconstruction team in northeastern Baghlan province, provincial governor Abdul Majeed said.
Friday's deaths bring to at least 24 the number of people killed since Tuesday at violent anti-US protests over the burning of Korans at the US airbase of Bagram, north of the capital. In Kabul, AFP photographers saw two bodies at one of multiple protest sites, but an interior ministry spokesperson said only that three people were wounded.
The protests flared after Friday prayers, where mullahs condemned "Infidels" for the desecration of Islam's holy book.
"Those who have committed this crime should be identified and should be publicly executed," said mullah Mohammad Ayaz Niazi at Kabul's Wazir Akbar Khan mosque.
"You have not just betrayed a nation, but you have played with the faith and sentiments of 1.7 billion Muslims worldwide, and you have trampled their holy book," he said, while urging that any protests should be peaceful.
Rallies also broke out in northern Kunduz province, as well in central Bamiyan and Ghazni and eastern Nangarhar, where one person died, AFP correspondents said.
Two US soldiers were shot dead by an Afghan soldier at a protest on Thursday. French, Norwegian and US military bases also came under attack, after insurgents exhorted their countrymen to kill foreign troops in revenge.
The US embassy in Kabul has been in lockdown for days, while extra security forces are protecting foreign missions and other strategic places, some armed with rocket-propelled grenades and heavy machine-guns.
Last April, 10 people were killed and a UN compound in the north was overrun during days of unrest unleashed by the burning of a Koran by American pastor Terry Jones in Florida.
The Afghan government and the US commander of the NATO mission in Afghanistan, General John Allen, called for calm and restraint in a country wracked by 10 years of war against hardline Islamist insurgents.
"Working together with the Afghan leadership is the only way for us to correct this major error and ensure that it never happens again," said Allen.
Government investigators urged Afghans to "avoid resorting to protests and demonstrations that may provide ground for the enemy to take advantage of the situation".