"We will respect freedom of the press, because media reporting will be useful to society and will be able to help correct the leaders' errors," Mujahid was quoted as saying. "Through this statement to RSF, we declare to the world that we recognise the importance of the role of the media."
He added: "Journalists working for state or privately-owned media are not criminals and none of them will be prosecuted. In our view, these journalists are civilians and moreover, are talented young people who constitute our richness."
Under the first period of Taliban rule in Afghanistan from 1996-2001, all media was banned except for the Voice of Sharia radio station "which broadcast nothing but propaganda and religious programmes," RSF recalled in its statement.
The group said "only time will tell" if the statement should be taken seriously and it pointed to around 100 media outlets having stopped operating since the Taliban's rapid advance in the country.
Asked about the fate of women journalists, Mujahid said that they would be allowed to keep working, providing they wear a hijab, or hair-covering.
He said a "legal framework" would be established and in the meantime they should "stay at home, without stress and without fear."
"I assure them they will go back to their jobs," he added.
Many analysts urge caution on taking Taliban commitments at face-value, given the group's history of reneging on agreements and their violent hostility to anyone seen as working against their interests.
The group is also seen as keen to project a more moderate image in order to gain international recognition.
Afghanistan has at least eight news agencies, 52 TV channels, 165 radio stations and 190 print publications, RSF said, citing figures from the Afghan Federation of Media and Journalists.
It has a total of 12,000 journalists, according to the same source.