August 19 is the day that Afghanistan celebrates its 1919 independence from British control.
How the Taliban handle the protests, which have included people tearing down white Taliban flags, according to media, could determine whether people put faith in their assurances that they have changed since their 1996-2001 rule, when they severely restricted women, staged public executions, and blew up ancient Buddhist statues.
In Asadabad, capital of the eastern province of Kunar, several people were killed during a rally but it was not clear if the casualties resulted from Taliban firing or from a stampede that it triggered, a witness said.
Protesters also took to the streets of the city of Jalalabad and a district of Paktia province, both also in the east.
On Wednesday, Taliban fighters fired at protesters waving flags in Jalalabad, killing three, witnesses and media reported. Media reported similar scenes in Asadabad and another eastern city, Khost, on Wednesday.
A Taliban spokesperson was not immediately available for comment.