Syrian and international human rights groups urged the world's top war crimes prosecutor on Tuesday to investigate the killing of more than 1,000 civilians during protests against Syrian President Bashar Al-Assad.

The prosecutor's office at the International Criminal Court said it had received the request but its jurisdiction could only cover crimes committed in Syria by nationals of ICC member states.

"We have documented a large number of deaths, injuries, forced disappearances and arbitrary detentions," said US-based lawyer Yaser Tabbara.

"These are crimes that can be categorised as crimes against humanity as they were state policy, widespread and systematic."

Syrian and international rights groups say they have drawn hope from the ICC prosecutor's speed in calling for the arrest of Libyan leader Muammar Gaddafi and others over the violence in Libya and a willingness to investigate Ivory Coast and Kenya.

Damascus has not signed the 2002 Rome Statue that set up the court, which means the ICC does not have jurisdiction in Syria, unless the UN Security Council refers it to the court.

Amnesty International called on the Security Council to refer Syria to the ICC.

"Given the violence that existed in Libya at the time and the evidence in respect to the commission of crimes in Syria, I think that the situation in Syria is just as serious, if not more so," said Philip Luther at Amnesty International.

European calls to have the UN Security Council formally rebuke Syria stalled in May when it became clear Russia would use its veto, but France says it is ready to ask for a draft resolution, despite Russia's threat.

Assad has made some reformist gestures, such as issuing a general amnesty to political prisoners and launching a national dialogue, but the NGOs hold him, his brother Maher Al-Assad and intelligence chief Ali Mamlouk responsible for the deaths.

"I escaped from Syria in 1981, when I was 17. I've been in a foreign country for 30 years now, while the regime in Syria is still the same," said Ibrahim Akkari, one of a small group of protestors who accompanied Tabbara to the ICC in The Hague to present the request. "Our people have had enough of it."