Jihadists shot down a Syrian warplane conducting strikes on the Islamic State group stronghold of Raqa on Tuesday, the Syrian Observatory for Human Rights monitoring group said.

"IS fighters fired on a military aircraft which crashed," the Britain-based group said.

"It is the first aircraft shot down since the regime launched air strikes against the jihadists in July following their declaration of a caliphate in late June," said the group, which relies on a wide network of doctors and activists for its reports.

Observatory director Rami Abdel Rahman told AFP that the plane was carrying out strikes on the IS stronghold of Raqa when it was hit.

It crashed into a house in the Euphrates Valley city, the sole provincial capital entirely out of Syrian government control, causing deaths and injuries on the ground, he added.

A photograph posted on a jihadist Twitter account purported to show the burnt-out wreckage of the plane.

"Allahu Akbar (God is greater), thanks to God we can confirm that a military aircraft has been shot down over Raqa," another account said, congratulating the "lions of the Islamic State".

The plane is far from the first government aircraft downed by opposition forces, but it comes after President Bashar al-Assad's regime stepped up its air campaign against IS in eastern Syria.

In recent weeks it has repeatedly targeted the group's Euphrates Valley strongholds in Raqa and Deir Ezzor provinces and jihadist-held areas of the northeastern province of Hasakeh.

- Missiles hit Damascus -

Elsewhere in Syria on Tuesday, the Observatory said at least 11 missiles had been fired at parts of Damascus by an Islamist rebel group, killing a child and injuring several people.

The missiles hit districts known as Christian or Alawite areas, or for being upscale residential districts, including Sabaa Bahrat, Malki, Abu Rumana, Qasaa and Mazze.

The rocket fire came a day after an Islamist rebel group warned it would begin a new campaign of fire against the capital targeting "presidential, military and security areas".

It said the rocket fire would be a response to the regime's "appalling massacres and vicious bombing" in rebel-held areas in Damascus and the surrounding province.

Syria forces have been pounding rebel-held areas outside the capital for weeks, with at least 11 people killed in the Hamouriya area, east of Damascus, in regime air strikes on Tuesday, the Observatory said.

Earlier, the Observatory said at least two members of regime forces were killed in clashes with rebels including Al-Qaeda affiliate Al-Nusra Front in Damascus province.

The fighting in Dakhaniya, near the eastern outskirts of Damascus, also killed 12 opposition fighters overnight.

Rebel forces seized the area near Jobar in east Damascus and adjacent to the opposition stronghold of Eastern Ghouta last week and regime forces are fighting to reclaim it.

In the capital, meanwhile, the Observatory said the toll in a failed rebel attempt to infiltrate a district adjacent to the Old City had risen to 11 opposition fighters killed.

They were killed in clashes after they entered the Midan neighbourhood through a sewer in the early hours of Monday, security sources said.

After fierce fighting in the capital in 2012, regime forces expelled rebel fighters from the heart of the city, but they remain in several strongholds on its outskirts.