Mr Gbagbo and Alassane Ouattara both say they won last month's election and have each named cabinet ministers amid a stand-off in the main city Abidjan. The UN, the West and African leaders all say Mr Ouattara was the victor.
There are fears that the dispute could reignite civil war in the world's largest cocoa producer.
About 50 people have been killed in recent days, according to UN human rights chief Navi Pillay. She said she had received reports of hundreds of people being snatched from their homes by people in military uniforms. Some were later found dead.