The Taliban have been trying to crush the protests, which were also held in Nangarhar, Khost and Kunar. Reuters news agency quoted a witness as saying that several people are said to have been killed in the Asadabad city for waving the national flag.
Social media is abuzz with videos and photos of men and women waving the country's national flag and chanting, "Our flag, our identity." Taliban reportedly opened fire at the protestors, but it remains unclear if the deaths were caused by the shots or stampede.
Taliban officials said they were celebrating their victory over the US on Afghanistan's Independence Day.
Meanwhile, thousands of Afghans are still attempting to escape the Taliban rule via Kabul airport. Evacuation centres have been set up by foreign embassies inside the airport compound.
According to Taliban and NATO officials, at least 12 people have lost their lives in and around the Kabul airport since Sunday when the city fell to the Taliban.