The Committee to Protect Journalists (CPJ) urges a Saudi-led bloc to drop its demand to shut media outlets funded by Qatar as a condition to lift the blockade against it.
In a letter directed to the leaders of Saudi Arabia, the United Arab Emirates, Bahrain and Egypt, the CPJ stressed it was not taking sides in the diplomatic dispute in the Gulf.
The CPJ, an independent organisation that promotes press freedom worldwide, said the demand to close the outlets, including Al Jazeera, showed "clear contempt for the principle of press freedom".
The media watchdog also pointed out that the demand violated "treaty commitments to the rights to free expression and to freely receive and impart information.
"[The demands] represent a clear attempt to interfere in the internal affairs of the countries where these media companies operate - under the guise of demanding that Qatar not interfere in other countries' internal affairs, thereby limiting the diversity of sources for information and views in the region."
Saudi Arabia, the UAE, Bahrain and Egypt cut diplomatic ties with Qatar and imposed sanctions on the country on June 5, accusing it of supporting "terrorism".
The allegation is rejected by Doha.
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After more than two weeks, the four Arab countries issued a 13-point demand list in exchange for the end of the anti-Qatar measures and gave a 10-day deadline, which expires on July 3.
The demands included the closure of all news outlets that Qatar allegedly funds, directly and indirectly, including Arabi21, Rassd, Al Araby Al Jadeed, Mekameleen and Middle East Eye.
The Committee to Protect Journalists, Human Rights Watch, Reporters Without Borders, the New York Times editorial board and The Guardian have all condemned the efforts to pressure Qatar into shutting down Al Jazeera.
David Kaye, the United Nations special rapporteur on freedom of opinion and expression, has also rejected the demand to close Al Jazeera, saying that such a move would be "a major blow to media pluralism".
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Al Jazeera has described the Saudi-led campaign as "nothing but an attempt to silence the freedom of expression in the region and to suppress people's right to information and the right to be heard".
"We are stunned by the demand to close Al Jazeera," Giles Trendle, the acting managing director of Al Jazeera's English-language service said. "Of course, there has been talk about it in the past, but it is still a great shock and surprise to actually see it in writing. It's as absurd as it would be for Germany to demand Britain to close the BBC."
Trendle said Al Jazeera is going to continue its "editorial mission of covering the world news in a fair and balanced way".
Sheikh Mohammed bin Abdulrahman Al Thani, Qatar's foreign minister, has said that Al Jazeera Media Network is an "internal affair" and there will be no discussion about its fate during the diplomatic crisis.