The Arab television network al-Jazeera reported a video had been released in which fighters from at least 14 brigades, including the Liwaa al-Tawhid and Jubhat a-Nusra groups, declared they had rejected the coalition in favor of pursuing an Islamic state in Syria.
China's Xinhua News Agency reported the video showed several members of rebel groups around a table with a bearded man sitting in the center, a black flag behind him and the Koran before him.
"We reject the conspiratorial project about the national coalition," the bearded man said, adding that "we have come to agree on the establishment of a fair and Islamic state.
"We reject any external project whether it was a coalition or a council imposed on us by any party."
Al-Jazeera said the video's authenticity had not been independently verified and a representative of Liwaa al-Tawhid told the network the video, though posted on the group's Facebook page, did not represent the leadership's position.
"This video was done by members of the group without referring back to the leadership. The leadership will issue a statement soon," he said.
Other opposition activists downplayed the import of the video.
"Whether this statement is true or not, the Syrian people are all supportive of the coalition," Mohammad Saeed of the Syrian Revolution General Commission said.
"These groups have no right to support or reject the coalition."
The Russian news agency RIA Novosti reported the 27 EU members in Brussels officially recognized the coalition as a legitimate representative of the Syrian people. Full diplomatic recognition, however, will be up to each EU member individually, which France and Italy have done.
Meanwhile, al-Jazeera said Egypt's official news agency reported Ahmad Mouaz al-Khatib, head of the newly formed Syrian National Coalition for Opposition and Revolutionary Forces, announced Monday the coalition will have its headquarters in Cairo.
"There is a decision by the coalition to make Egypt its main headquarters," the Middle East News Agency quoted Khatib as saying.
The Egyptian Foreign Ministry said in a statement Egypt was prepared "to offer all means of assistance to the Syrian coalition in the coming period."
Tens of thousands of Syrians have died since protests against the government of President Bashar Assad began in March 2011 and deteriorated into civil war.
The Syrian Network for Human Rights in London issued a statement Monday noting the majority of Palestinians residing in Syria have taken part in the Syrian revolution by participating "very effectively during protests and marches [and] many Palestinian activists also stood out in Homs, specifically in the medical aid and relief work" despite being targeted by the Syrian army.