A dozen people told Reuters there had been unannounced visits from the Taliban in the past 24 hours, from the capital Kabul to Lashkar Gah in the south and northern Mazar-i-Sharif.
They did not wish to give their full names, for fear of reprisals.
As well as encouraging people to work, some said they also felt the checks were designed to intimidate and instil fear of the new leadership.
A Taliban spokesperson did not immediately respond to a request for comment on the visits.
Many businesses in the capital Kabul remain closed and large parts of the city have been deserted since the Taliban captured it on Sunday at the end of a lightning sweep across the country.
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The only major traffic in the usually congested capital was at the airport, where people are trying to flee the country aboard diplomatic evacuation flights, residents said.
Seventeen people were injured in a stampede there on Wednesday, and the Taliban said they fired in the air to disperse crowds.
At Tuesday's press conference, Taliban spokesman Zabihullah Mujahid said the Islamist movement was seeking good relations with other countries to allow economic revival and "prosperity to come out of this crisis."
But some are sceptical of the Taliban, who during their previous rule from 1996-2001 dictated that women could not work and girls were not allowed to attend school, and imposed punishments such as public stoning.
Presenter Shabnam Dawran said in a video shared on Twitter on Wednesday that she was turned away from her job on Afghanistan's state-owned Radio Television Afghanistan.
"They told me that the regime has changed. You are not allowed, go home," she said.
The Taliban and the news organisation did not immediately comment on the incident.
Wasima, who watched the Taliban's news briefing with her two daughters, said she feared that opportunities for women would diminish under the Taliban, even if they were now urging her back to work.
"The Taliban say women should work but I know for a fact that opportunities will shrink," she said.
