Malcolm Ranjith, the archbishop of Colombo, said he was urging President Mahinda Rajapakse and the main ethnic Tamil party to hammer out a political settlement or risk an international probe.
"Foreigners should not tell us what to do... We are not a pack of fools," the cardinal said.
"But if we do not resolve these issues, then we open ourselves to foreign intervention.
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Sri Lanka has resisted international calls to investigate allegations that up to 40,000 ethnic Tamil civilians were killed by security forces in the final months of fighting in 2009.
At a Commonwealth summit hosted by Colombo last month, Britain's Prime Minister David Cameron warned that he would push for an international inquiry under the auspices of the UN unless Sri Lanka ensures accountability by March.
In a pastoral letter, the church warned that failure on the part of Colombo to ensure accountability for alleged war crimes could trigger international investigations that will be a "serious threat to the sovereignt