Sultan Munadi was killed during a British Special Forces raid on the compound where they were being held early on Wednesday morning.
Stephen Farrell, a reporter for The New York Times, was rescued unhurt.
Vincent Brossel, regional head at Reporters Without Borders, told Al Jazeera: "It is not clear at all what happened and that is why we asked the Afghan Journalists Organisation to appeal to the British government to launch an investigation.
"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 amongst 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."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, northern Afghanistan.
Source: Al Jazeera (English)