The protest was outside a police station, and Mr Naqdi and Mr Daryabi said they were taken inside the station and severely beaten.
“They were hitting me with extreme force that I really thought that this was the end of my life,” Mr Naqdi told CNN on Friday.
“They have hit me on my arm with extreme force that I could not move it during the last two days … it has got better.
“My left eye has been hurt seriously that it is still red, and I am worried, my left ear can’t receive any hearing. It has a buzzing noise. I was given four or five very hard slaps on my face.”
Mr Naqdi said they they stepped on his head.
“They were pressing their foot on my head, my face was on the mosaic floor, and I was trying to pull myself due to the pain and to tell them to hit me on all sides and not just hit me on my back,” he said.
“For that reason, my face was bloodied.”
The video journalist said he felt like his neck or back might break.
“They were using such violence that one was holding me by my head and face and another one was holding me by my waist,” he said.
“My hands and feet were tied and one of them was pushing my legs like a sling.”
“When the Taliban forces arrested us and took us to the police station, they continuously tortured me for approximately 10 minutes even though I was not in state to remember the exact time,” Mr Daryabi said.
“They hit me with whatever they could grab hold of.”
He said it was possible that “from now on the Taliban threaten and torture journalists”.
“They declared to the journalists in a press conference that they will be granted permission to continue with their activities but only under the Islamic rules,” he said.
“I believe those threats are still present. The journalists will not stop, they are a different sector of the society, and they are people who convey the voice of the population.
“They become the voice of the people.”
CNN has reached out to the Taliban but has not received a comment at the time of this writing.
Zaki Daryabi, Editor-in-Chief of EtilaatRoz, told CNN he hoped that “in the first step, the Taliban leadership would respond to this continuous and brutal torture of our colleagues; and they would reprimand those who had committed this crime and act of torture in police district three; they would subject them to [legal] prosecution.”
“Secondly, we expected the Afghan and international media not to present this as an attack on EtilaatRoz [daily]; to present it as an attack on all media and discussion of freedom of expression,” He said.
Nemat Naqdi and Taqi Daryabi were among at least 14 journalists detained over the course of two days while covering protests in Kabul, according to the Committee to Protect Journalists.
At least six of the journalists “were subject to violence during their arrests or detention,” according to CPJ.
“The Taliban must immediately cease detaining journalists in Afghanistan, end the use of violence against them, and allow the media to operate freely and without fear of reprisal,” CPJ said in a statement.
The protests took place in the Dasht-i-Barchi area of Kabul, mostly inhabited by people from the minority Shia Hazara ethnic group known to have been targeted by the Taliban in the past.
Some protesters were also detained but it is not yet clear how many.
Witnesses have estimated the crowds at the protests at between 300 and 500 â€” some of the largest demonstrations since the Taliban took control of Kabul.