"We must know exactly what happened because it is not clear. We don't have any clear hypothesis, and we need the truth because there is a lot of anger among Afghan journalists.
"He was a very respected and senior journalist in Afghanistan, so we must know the truth."
Farrell, in a report on the newspaper's website, said: "We were all in a room, the Talibs all ran, it was obviously a raid.
|Farrell had travelled to Kunduz to report on Nato's bombing [The New York Times via AFP]
"There were bullets all around us. I could hear British and Afghan voices."
Farrell said Munadi went forward shouting "Journalist!" but fell in a burst of gunfire, which Farrell said could have been from the rescuers or the kidnappers.
Farrell, a 46-year-old with dual Irish-British nationality, is the second New York Times journalist to be captured in less than a year.
David Rohde was held in Afghanistan and Pakistan for seven months until June, when the newspaper says he escaped from captivity in Pakistan.
Farrell and Munadi were abducted earlier this month while attempting to visit the scene of a Nato air attack in Kunduz in northern Afghanistan.
One British service member died during the early morning raid, Gordon Brown, the British prime minister, announced.
Afghan journalists are said to be furious over the death of Munadi, a 34-year-old father of two who was working in Afghanistan on a break from university in Germany, saying negotiations were under way that would have freed the two.
Mohammad Sami Yowar, a spokesman for the Kunduz governor, said British special forces had dropped down from helicopters on to the house where the two journalists were being kept.
A Taliban commander who was in the house was killed, along with the owner of the house and a woman who was inside, Yowar said.
Farrell and Munadi had travelled to Kunduz to investigate the Nato raid that is believed to have killed scores of civilians.
Afghan officials said about 54 people died in a bombing on two tankers hijacked by Taliban fighters.
There were reports that villagers who had come to collect fuel from the tankers were among the dead, and Farrell had wanted to interview villagers.