About 150km east of the capital in Jalalabad, protests against the Taliban provided an early test of the group's promise of peaceful rule.
After seizing power over the weekend, the Taliban said they would not take revenge against old enemies and would respect the rights of women within the framework of Islamic law.
Two witnesses and a former police official told Reuters that Taliban fighters opened fire when residents tried to install Afghanistan's national flag at a square in the city, killing three and injuring more than a dozen.
Taliban spokespeople could not be reached for comment.
NOT A DEMOCRACY
A new government to replace that of President Ashraf Ghani, who is in exile in the United Arab Emirates, may take the form of a ruling council, with Taliban supreme leader Haibatullah Akhundzada in overall charge, a senior member of the group said.
But Afghanistan would not be a democracy. "It is sharia law and that is it," Waheedullah Hashimi told Reuters.
Ghani, who has been bitterly criticised by former ministers for leaving Afghanistan as Taliban forces swept into Kabul on Sunday, said he had followed the advice of government officials. He denied reports he took large sums of money with him.
"If I had stayed, I would be witnessing bloodshed in Kabul," Ghani said in a video streamed on Facebook, his first public comments since it was confirmed he was in the UAE.
About 5,000 diplomats, security staff, aid workers and Afghans have been evacuated from Kabul in the past 24 hours and military flights will continue around the clock, a Western official told Reuters.
"Everyone wants out," said a member of an Afghan family after they arrived in Germany. "Every day is worse than the day before. We saved ourselves but we couldn't rescue our families."
The Taliban have suggested they will impose their laws less severely than during their former rule, and a senior official said on Wednesday that the group's leaders would be less reclusive than in the past.
"Slowly, gradually, the world will see all our leaders," the senior Taliban official told Reuters.
"DEEDS NOT WORDS"
Hashimi, who has access to the Taliban's decision-making, said the role of women, including their right to work and education and how they should dress, would ultimately be decided by a council of Islamic scholars.
"They will decide whether they should wear hijab, burqa, or only (a) veil plus abaya or something, or not. That is up to them," he told Reuters.
Under the Taliban's 1996-2001 rule, women were prevented from working, girls were not allowed to go to school and women had to wear all-enveloping burqas to go out.
Echoing comments by world leaders, British Prime Minister Boris Johnson said the Taliban would be judged "by its actions rather than by its words".
Many Afghans are sceptical of the Taliban promises.
"My family lived under the Taliban and maybe they really want to change or have changed, but only time will tell and it's going to become clear very soon," said Ferishta Karimi, who runs a tailoring shop for women.
The Taliban seized Kabul on Sunday as Western forces withdrew under a deal that included a Taliban promise not to attack them as they leave.
US President Joe Biden has faced a barrage of criticism about the withdrawal, including from British lawmakers on Wednesday who called Afghanistan's collapse into Taliban hands a failure of intelligence, leadership and moral duty.
Biden has said he had to decide between asking US forces to fight endlessly or follow through on the withdrawal deal of his predecessor, Donald Trump.
US Senate Republican leader Mitch McConnell, during an appearance in his home state of Kentucky, pledged to keep the "heat" on Biden to rescue U.S. allies in Afghanistan and said Congress would consider allocating more money to help if needed.
He also dismissed the idea of a "new" Taliban, calling the militants "barbarians".