A draft of the letter said that the situation in Syria should be referred to the Hague-based war crimes tribunal "without exceptions and irrespective of the alleged perpetrators."
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"At the very least, the council should send out an unequivocal message (...) announcing that it intends to refer the situation to the ICC unless a credible, fair and independent accountability process is being established in a timely manner" by Syria, it continues.
The letter cites the findings of a UN expert panel documenting summary executions, torture and sexual violence that has occurred since the start of the uprising in March 2011.
It also notes repeated appeals by the UN's top human rights official and resolutions by the global body's Human Rights Council calling for ICC referral.
The draft letter was signed by Switzerland's ambassador to the United Nations in New York on behalf of dozens of countries including Britain and France, two of the Security Council's five permanent members.
The other three permanent members – the United States, China and Russia – had not signed the draft.
Russia insists that Syria must be left to resolve the conflict independently. Moscow's priority "Is to immediately cease all violence and bloodshed and deliver humanitarian assistance to the Syrians, including IDPs and refugees," the Russian Foreign Ministry said in a statement.
A spokesman for Switzerland's UN mission in New York said the letter would be submitted to the Security Council on Monday.
Adrian Sollberger said Switzerland first proposed such a move in June 2012, and that it now had the backing of more than 50 countries from all regions of the world, giving the call sufficient political weight.
"The manifold allegations of crimes against humanity and war crimes in Syria must be investigated and those responsible among all the parties of the conflict must be brought before a court," he said.
The Security Council is the only body that can refer Syria to the ICC because the country itself hasn't ratified the international convention that established the tribunal.
The UN's human rights office issued a report last week estimating that at least 60,000 people have died in Syria since the start of the conflict.
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