Several others were injured in the confrontation, which took place in a neighbourhood loyal to Mr Gbagbo’s rival, Alassane Ouattara, in Abidjan.
Mr Ouattara is widely recognised as the victor of presidential polls last year, but Mr Gbagbo refuses to cede power.
Tensions have been high in the West African nation since the elections.
Hundreds of youths gathered in the neighbourhood of Abobo before security forces opened fire and used tear gas in an effort to disperse them.
A resident told AFP news agency that forces had “fired into the crowd leaving people running for cover, but they chased them”.
‘Store raided’
One of those killed was a woman who was hit by a stray bullet, witnesses and an official told Reuters news agency.
Protesters also raided the department store of a Lebanese businessmen who is seen as close to Mr Gbagbo.
The neighbourhood of Abobo has often been the scene of violent clashes between security forces and civilians.
At least 300 people have been killed in violence since the polls, mostly supporters of Mr Ouattara killed by pro-Gbagbo forces, the United Nations says.
November’s presidential vote was supposed to reunify the world’s largest cocoa producer, which has been divided between north and south since a conflict in 2002.