With international frustration growing over the big powers’ inability to take any action on Syria, some countries are urging the United Nations Security Council to refer Syria’s mounting humanitarian and human-rights disaster to the International Criminal Court (ICC).

The demand for international judicial action came Monday in a letter authored by Switzerland and signed by 56 other countries. The call coincided with fresh alarms from international rights organizations concerning what one called the “staggering” humanitarian tragedy unfolding in Syria.

One organization issued a report finding a rise in the use of sexual violence in the nearly two-year-old civil war, with growing numbers of women and girls fleeing the fighting claiming to be the victims of gang rapes – sometimes committed in front of other family members.

Another group that tracks the fighting reported that Monday was the deadliest day of the war yet for children, with reports of 21 Syrian children killed in attacks.

The latest examples of violence, in a war that UN authorities say has already claimed more than 60,000 lives, served as a backdrop to the demand for referral of the Syrian crisis to the ICC.

Some skeptics of the ICC route say that, while the Swiss letter reflects understandable desperation in the international community to find a way to overcome the Security Council impasse on Syria, going to the court in The Hague would have no effect on the civil war. Other critics say the ICC route could actually put off resolution of the conflict by convincing Syrian President Bashar al-Assad that his only alternative is to stay put and fight.

But others say international judicial action can have an impact, and they point to the Balkans war of the 1990s as an example. In a statement backing ICC referral, Human Rights Watch (HRW) said the record in cases like the Balkans “confirms that criminal indictments of senior political, military, and rebel leaders can actually strengthen peace efforts by delegitimizing and marginalizing those who stand in the way of the conflict’s resolution.”

One roadblock to ICC referral is that Syria is not a signatory to the treaty that established the international court. That means the Security Council would need to make the referral for the international court to gain jurisdiction over crimes committed in the Syrian conflict. The Security Council has been paralyzed by divisions over the fate of President Assad’s regime, with permanent council members Britain, France, and the US saying Assad must step down and Russia and China resisting – to the point of vetoing – any attempts at action on Syria.

Supporters of a referral hold out hope that China and Russia, which profess not to be taking sides in the conflict, could be persuaded that ICC action would not specifically target Assad but would be aimed at war criminals on all sides. “A referral would be unbiased and give the ICC jurisdiction to investigate crimes committed by the government and the opposition,” says Balkees Jarrah, HRW’s international justice counsel. The point would be to “send a message” to all sides that “abuses could land them in a prison cell in The Hague.”

A report issued Monday by the New York-based International Rescue Committee (IRC) finds that a growing number of women fleeing Syria for refuge in neighboring countries are citing sexual violence as a major reason for leaving the country.

More than 600,000 Syrians are estimated to have fled to Turkey, Jordan, Lebanon, Iraq, and Egypt. Thousands of them are in makeshift camps that provide little protection from a wet and freezing winter.

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But many women say even those poor conditions are preferable to falling prey again to sexual violence or to living in fear of it happening to them or their daughters. The IRC report says such fears make sexual violence the primary factor cited by Syrian women in Jordan and Lebanon for their decisions to flee their country.

Also on Monday, the London-based Syrian Observatory for Human Rights listed separate incidents around the country that resulted in the deaths of 21 children – including a 6-month-old infant. The observatory, an opponent of the Assad regime, said eight of the deaths occurred in an airstrike on the village of Moadamiyat southwest of Damascus.