The UN High Commissioner for Human Rights has recommended that Syria be referred to the International Criminal Court in the Hague.
Navi Pillay told the UN Security Council that over 5,000 people are thought to have been killed in nine months of unrest in Syria.
The latest figure reported to the UN is 1,000 higher than those announced by Ms Pillay just 10 days ago.
She said the toll includes civilians, army defectors and those executed for refusing to shoot civilians, but not soldiers and other security personnel killed by opposition forces.
Ms Pillay said 14,000 people are thought to have been arrested and a further 12,400 have fled to neighbouring countries.
The Syrian government has said more than 1,100 members of the army, police and security services have been killed.
A wave of protests against four decades of Assad family rule erupted in Syria in mid-March, inspired by popular uprisings in Tunisia, Egypt, Yemen and Libya.
A violent security crackdown has failed to halt the unrest, which has turned bloodier in the last few months as defecting soldiers join armed civilians in fighting back in some areas.
