The leader of the main opposition Rally of Republicans Party, Alassane Ouattara, is not present although delegates from his party are attending.
Also absent are the former military leader General Robert Guei, and the man he toppled in a coup in 1999, former President Henri Konan Bedie.
However, leaders in the region including the presidents of Ghana and Mali are in the country to back President Laurent Gbagbo's efforts.
The conference was called to address the political crisis in what was once one of Africa's most stable countries.
And the Malian and Ghanaian leaders made impassioned pleas to the politicians of Ivory Coast to resolve their differences in the interests of the entire region.
But a military coup in 1999 and the manipulation of ethnic differences by politicians has caused two years of unrest and several hundred deaths.
Conditions
Mr Ouattara, in exile in France, has been excluded from standing in presidential elections on the grounds that he is a foreigner.
His supporters, who say he is Ivorian, said he would not attend the conference unless this policy was changed.
"The situation is getting better," Mr Ouattara told AFP news agency by telephone from Paris.
"It seems that political prisoners are being freed. My own demand for safety guarantees has been taken into account by the authorities.
"But I'm not going to the opening of the forum... since my political and civic rights are still not recognised by the authorities."
Other political leaders put different conditions on their attendance.
Applause
The two impassioned speeches by Ivory Coast's neighbouring presidents were warmly applauded by the audience of several hundred people who attended the forum.
President John Kuffour of Ghana said he had watched with deep anxiety as Ivory Coast seemed to disintegrate along tribal lines and amid religious intolerance.
President Alpha Oumar Konare of Mali referred to the genocide in Rwanda and warned Ivorians to take great care because, he said, catastrophe can come quickly if you don't maintain dialogue.
Our West Africa correspondent Mark Doyle says the Ivory Coast is a classic example of what can go wrong in Africa when politicians manipulate ethnic differences in the pursuit of power.
The organiser of the conference, former prime minister Seydou Diarra, is reported to have started hinting that the talks may continue beyond the scheduled closing date in two months time.