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In a private briefing to the council on Monday, Pillay said more than 5,000 Syrians have now been killed in the government's crackdown on protests.
Pillay said 300 children have died since the uprising began in March, and that an estimated 14,000 Syrians had been arrested.
She recommended the case be referred to the International Criminal Court.
Following Pillay’s comments, France's envoy to the UN, Gerard Araud, says the UN Security Council was "morally responsible" for the killings in Syria, Agence France Presse reported.
Russia's ambassador, Vitaly Churkin, accused western nations of discouraging dialogue with the Syrian government.
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Meanwhile activists said another 20 people were killed in Syria on Monday in Homs, Hama and the capital Damascus, the Guardian reported.
The violence came as local elections were conducted. Turnout was understood to have been very low, amid an opposition boycott.
Reports said pro-democracy activists had also launched a civil disobedience campaign and a general strike.
The government said the elections were part of a package of democratic reforms.
The EU has imposed 10 rounds of sanctions on the Syrian government, which has also been suspended by the Arab League.
But the UN has not yet passed a resolution condemning Damascus.