The groups, in a statement, also called for the opposition to unite under an "Islamic framework," the BBC reported Wednesday.
In their joint statement, the Islamist groups said, "All groups formed abroad without having returned to the country do not represent us."
The presence of Islamist rebel forces has grown in the conflict in Syria. They are believed to command tens of thousands of fighters.
In a video statement published online Tuesday, 11 of the most powerful Islamist groups said they reject the concept that opposition leadership could emerge from any organization based outside Syria that was not working with those within the ravaged country.
The Western-backed National Coalition, based in Istanbul, Turkey, was formed in November 2012 and is recognized by more than 100 countries as the legitimate representative of the Syrian opposition.
"These forces feel that all groups formed abroad without having returned to the country do not represent them, and they will not recognize them," the statement said.
The statement also called on military and civilian forces to rally under "a clear Islamic framework based on Sharia [Islamic law], which should be the sole source of legislation."
Also Wednesday, U.N. inspectors returned to Syria to resume their investigation into the alleged use of chemical weapons during the conflict. Last week, they confirmed that the nerve agent sarin was used in an attack on several Damascus suburbs Aug. 21 in which hundreds of people were killed.
The inspectors plan to visit Khan al-Assal, Sheikh Maqsoud and Saraqeb, where chemical attacks on a smaller scale allegedly occurred earlier this year, the BBC said.
Six civilians were killed and 11 others were injured what government-run media called a terrorist suicide bombing in the Damascus neighborhood of al-Tadamun.
SANA reported that 10 people were injured after terrorists – the word the government uses to describe rebels -- launched mortar shells on al-Abassiyeen and Zablatani neighborhoods in Damascus.
Three other civilians, including a woman, were killed in a mortar attack in Ain al-Tineh, SANA said.
In Moscow, a senior Russian diplomat told lawmakers a U.N. resolution may include military action against Syria but only as a possible response to chemical disarmament non-compliance.
"There can be no talk of any automatic application of sanctions or, especially, [a use of] force," Deputy Foreign Minister Sergei Ryabkov told Russian lawmakers in the Parliament's lower house.
The part of the U.N. mandate that permits military force to "restore international peace and security" "can be mentioned only as an element of a possible set of measures ... if any actions such as refusal to cooperate or non-compliance with obligations are identified," he said.
Washington and Moscow agreed Sept. 14 on a plan to seize and destroy Syria's chemical weapons, which averted an imminent U.S. attack on Syrian military sites. But the countries are at odds over how to enforce the initiative at the U.N. Security Council.
U.S. President Barack Obama told the U.N. General Assembly Tuesday, "The evidence is overwhelming that the Assad regime used such weapons on Aug. 21."
Obama added it was "an insult to human reason -- and to the legitimacy of this institution -- to suggest that anyone other than the regime carried out this attack." He said the Security Council resolution being worked out must include "consequences" for Syria if it fails to disarm itself of chemical weapons.
"If we cannot agree even on this, then it will show that the U.N. is incapable of enforcing the most basic of international laws," he said. "On the other hand, if we succeed, it will send a powerful message that the use of chemical weapons has no place in the 21st century, and that this body means what it says."
U.S. officials described the session to The Washington Post as very productive and substantive, with Kerry and Lavrov refining a draft text.
They would not say if the dispute over enforcing the chemical weapons deal was resolved or when they expected the resolution to be ready for a Security Council debate and vote.
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