Key Syrian Islamist rebel groups say they do not recognise any foreign-based opposition group, including the Syrian National Coalition.

"The National Coalition and the proposed government under [recently chosen] Ahmad Tomeh does not represent us, nor do we recognise it," 13 of Syria's most powerful rebel groups said in a joint statement late on Tuesday.

The groups include members of the main rebel Free Syrian Army, as well as Liwa al-Tawhid, the main rebel force in the northern province of Aleppo, and Jabhat al-Nusra, an al-Qaeda-linked group.

The UN Security Council blacklisted al-Nusra Front as an alias of al-Qaeda in Iraq in May, while the US State Department had designated the group as a terrorist organisation in December last year.

Ahrar al-Sham also signed on, as did the 19th Division, a significant but relatively new addition to the mainstream FSA.

In their statement, they also called for Islamic law to be applied.

"These forces call on all military and civilian groups to unite in a clear Islamic context that... is based on sharia [Islamic] law, making it the sole source of legislation," it said.

They called for "unity" and "to reject division... putting the interest of the [Islamic] nation over the interest of each group".

Rebel infighting

The statement comes amid an escalation of violence pitting fighters from various factions across the rebel spectrum against another al-Qaeda front group, the Islamic State of Iraq and the Levant (ISIL).

Rebel groups have increasingly been fighting amongst themselves in recent weeks.

The ISIL, a US-designated "terrorist organisation", announced last week it would "go to war" against two other rebel groups in the town of al-Bab, in Aleppo governorate.

More than a dozen fighters from the group were killed in the northern city of Hazano on Sunday, close to the border with Turkey, during clashes with other rebels. An uneasy truce agreed to last week temporarily ended fighting between ISIL and the Northern Storm brigade in the town of Azaz, near Aleppo.

ISIL and Jabhat al-Nusra have themselves come into conflict: On Saturday, fighters from the two groups clashed in the eastern province of Hasaka, according to the Syrian Observatory for Human Rights, killing at least two people.

"It's the hardest fighting we have ever seen between Salim Idriss's elements of the Free Syrian Army and the Islamic State of Iraq and the Levant," an unnamed US official told the Reuters news agency, referring to the general who commands the FSA.

"It's a slog."