Taliban officials have said the service will resume from Saturday, after being suspended since their takeover and the fall of the previous government in August.
The decision to halt that service led to many who were desperate to leave the country being stranded.
“I have come to get a passport but, as you can see here, there are lots of problems, the system is not working,” one applicant, Mahir Rasooli, told Reuters outside the office.
“There is no official to answer our questions here to tell us when to come. People are confused.”
A spokesman for Taliban officials running the passport department did not respond to requests for comment.
Poverty and hunger have become worse since the militant group took over Afghanistan, which was already suffering because of drought and the Covid-19 pandemic.
Billions of dollars worth of humanitarian aid has been frozen by much of the international community, and half a million people have been displaced in recent months, according to the United Nations, and that number will grow if health services, schools and the economy break down.
The hundreds who descended on the passport office came despite advice that distribution of passports would only begin on Saturday, and initially only for those who had already applied.
The crowd pressed against a large concrete barrier, trying to hand documents to an official in a scene reminiscent of the chaos at Kabul airport in the last stages of evacuation after the withdrawal of US troops.
The official urged them to return home and come back on Saturday.
“I am here to receive a passport, but unfortunately I couldn't,” said a man in the crowd, Ahmad Shakib Sidiqi. “I don't know what we should do in this condition.”
The bleak economic outlook drives the desire to leave, Mr Sidiqi and Mr Rasooli told Reuters.
“There is no job and the economic situation is not too good, so I want to have a good future for my kids,” Mr Rasooli said.
After the Taliban’s swift capture of Kabul in August, the world has waited with bated breath to see if the hard-won gains made by women and girls over the past 20 years would be upheld.
Last week, the Taliban said classes would resume for boys in year seven and above, but they made no mention of girls going back to school, effectively locking a large portion of Afghanistan's children out of the classroom.
Mr Sidiqi said he wanted a passport to accompany a member of his family to neighbouring Pakistan to seek medical treatment and that they had no choice but to leave.
“We have to leave Afghanistan,” he said. “It is a bad situation in Afghanistan – no job, no work. It is not a good condition for us to live.”
The Taliban have said they welcome international aid, although many donors froze their assistance after the group took power.