Seven people were killed in the western province of Herat, officials said.
Another protester died in the Pul-e-Khumri district of Baghlan province when a reconstruction office came under attack.
On Thursday US President Barack Obama apologised to the Afghan people, saying the burnings were a “genuine mistake”.
On Friday, a group of demonstrators tried to attack the US consulate in Herat, burning police vehicles and leaving several officers injured, security sources told the BBC.
Three people were killed in the city, with another four reported dead in other parts of Herat province.
Thousands are out in Herat and there are demonstrations in several places around the city. There are different groups out in force and some of the protests have turned violent. At the hospital we saw one body, and several other people who had been injured in the violence.
At least one group were trying to get into the US consulate, in the north of the city. We heard gunfire from security forces as they tried to stop the angry crowd.
The protests began after Friday prayers and people who had gathered in all the mosques in different part of the city streamed out and chanted slogans, expressing their fury at what happened.
The latest deaths bring the toll from protests in recent days to at least 20, including two US soldiers.
Protests were reported around the country on Friday: