The move highlights the struggle over the direction of the rebellion at a time when the opposition is trying to gain the West's trust and secure a flow of weapons to fight the regime.
The rising profile of the extremist faction among the rebels could doom those efforts. Such divisions have hobbled the opposition over the course of the uprising, which has descended into a bloody civil war.
According to activists, nearly 40,000 people have been killed since the revolt began 20 months ago. The fighting has been particularly extreme in Aleppo, Syria's largest city and a major front in the civil war since the summer.
Salman Shaikh, director of The Brookings Doha Centre in Qatar, said the Islamists' declaration will unsettle both Western backers of the Syrian opposition and groups inside Syria, ranging from secularists to the Christian minority. "They have to feel that the future of their country could be slipping away," Mr Shaikh said. "This is a sign of things to come the longer this goes on. The Islamist groups and extremists will increasingly be forging alliances and taking matters into their own hands."
The West is particularly concerned about sending weapons to rebels for fear they could end up in extremists' hands.
The Islamists' announcement, made in an online video, shows the competing influences within the rebellion, between religious hardliners who want to create an Islamic state in Syria - including foreign al Qaida-style jihadi fighters - and the newly formed Syrian National Coalition, which was created earlier this month in hopes of uniting the disparate groups fighting Assad's regime.
The National Coalition was formed under pressure from the United States, which sought a more reliable partner that nations could support. In the new video, 13 Islamic radical factions denounced the coalition as a foreign creation.
Most important among them were the al-Tawheed Brigade, which is one of the largest rebel groups operating in Aleppo, and Jabhat al-Nusra - Arabic for "the Support Front" - which is mainly made up of foreign jihadi fighters. Jabhat al-Nusra has become notorious for suicide bombings targeting regime and military facilities and is at the forefront of fighting in Aleppo.
"We are the representatives of the fighting formations in Aleppo and we declare our rejection of the conspiratorial project, the so-called national alliance," an unidentified speaker said in the video. "We have unanimously agreed to urgently establish an Islamic state."