"Any act contrary to the values that the Syrian people have paid their blood and lost their homes to will not be tolerated, the abuser will be punished severely even if they are associated with the Free Syrian Army," the main rebel group said in a statement.
The gruesome video, in which the rebel fighter leans over a uniformed body, cuts out organs and then holds one up to his mouth, has prompted an outcry around the world and has thrown the spotlight on war crimes allegations against the opposition.
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The Free Syrian Army (FSA) said field commanders had been instructed "to begin a prompt investigation into the matter in which the perpetrator will be brought to justice".
Investigations would also be held into whether the rebel in the video is a member of the Free Syrian Army or not, it said.
US State Department spokesman Patrick Ventrell said Washington had "raised this gruesome act in our recent conversations with leaders of the Supreme Military Council".
They "assured us that they do not support such actions and that this is not representative of the vast majority of the armed opposition," he added.
But UN High Commissioner for Human Rights Navi Pillay demanded a probe into the growing number of allegations of torture, summary executions and other abuses by rebel fighters.
The Free Syrian Army in its statement stressed that it was committed to "freedom and the rule of law for all of the people of Syria whoever they maybe and whatever their religious or ethnic description".
