UNITED NATIONS — Atrocities by the Syrian government “far outweigh” crimes by the opposition fighters and Syrian President Bashar Assad’s regime is “mostly responsible” for the human rights offenses in the three-year war, the U.N. human rights chief said Tuesday.

High Commissioner for Human Rights Navi Pillay said both sides’ abuses should be documented and brought to the International Criminal Court, “but you cannot compare the two. Clearly the actions of the forces of the government far outweigh the violations – killings, cruelty, persons in detention, disappearances, far outweigh” those by the opposition.

She appeared to be referring to a report in March by the U.N. Human Rights Council’s commission of inquiry on war crimes in Syria, which found there was complete impunity for abuses and said that responsibility appears to reach to the top of the government.

Pillay, who briefed the U.N. Security Council on Tuesday, has been pushing for an ICC war crimes prosecution since 2011. The council would have to refer the case to the ICC, but Russia and China, both permanent veto-wielding council members, have shielded Damascus from any serious council sanctions.

This month’s holder of the rotating council presidency, Nigerian Ambassador U. Joy Ogwu, noted that the council remains deadlocked on a referral to the International Criminal Court.

France had asked Pillay to brief the council on Syria, but Russia objected to putting the spotlight on its Middle East ally. As a compromise, Russia allowed Pillay to be invited to speak on an array of crises, including Syria, Central African Republic, Mali, Libya and South Sudan.