Islamic State has taken control of 90 per cent of a Palestinian refugee camp on the Damascus outskirts where 18,000 civilians have suffered years of bombing, army siege and militia control, a monitoring group said on Saturday.

The hardline group's offensive in Yarmouk gives it a major presence in the capital. Islamic State, the most powerful insurgent group in Syria, is now only a few kilometers from President Bashar al-Assad's seat of power.

The United Nations has said it is extremely concerned about the safety and protection of Syrians and Palestinians in the camp. Civilians trapped there have long suffered a government siege that has led to starvation and disease.

"The situation in Yarmouk is an affront to the humanity of all of us, a source of universal shame," UN Relief and Works Agency (UNRWA) spokesman Chris Gunness said.

"Yarmouk is a test, a challenge for the international community. We must not fail. The credibility of the international system itself is at stake," he said.

The Syrian Observatory for Human Rights, which monitors the conflict from Britain, said Syrian air force jet bombed the camp on Saturday.

The Islamic State on Wednesday launched an attack on other groups of fighters in Yarmouk, in particular Aknaf Beit al-Maqdis, an anti-Assad militia of Syrians and Palestinians from the camp.

Islamic State supporters posted photos on social media of the severed heads of two men they said had been beheaded after fighting for Aknaf Beit al-Maqdis.

The Observatory said Islamic State and al Qaeda's official Syria wing, the Nusra Front, made gains overnight, pushing into the northeast of the district, close to central Damascus. They now control 90 percent of the camp, it said.

Tayseer Abu Baker, head of the Palestinian Liberation Front in Syria, part of the Palestine Liberation Organization, told Reuters over the phone that Islamic State had killed 21 people including fighters and civilians since Friday.

"Some families are trying to exit the camp but with Islamic State snipers on rooftops of high buildings that is very difficult," he said. He added Islamic State had kidnapped at least 74 people from the camp and that civilians were trying to flee.

Reuters cannot independently verify reports in Syria due to security and reporting restrictions.

Islamic State rules swathes of eastern Syria and Iraq and is the target of a U.S.-led campaign of air strikes.

Yarmouk was home to half a million Palestinians before the Syrian conflict began in 2011. The war has killed 220,000 people and displaced millions.

Government officials could not be reached for comment. Syria's state news agency Sana said terrorists in the camp had prevented aid from reaching civilians. It added the army had encircled Yarmouk.-Reuters