The last-ditch effort comes after West African leaders threatened military intervention, after an emergency summit of the regional Economic Community of West African States, or Ecowas.
Gbagbo's spokesman branded the move a "Western plot directed by France".
It warned that military action would put at risk millions of immigrant workers in Cote D'Ivoire.
Despite a decade of crisis, the country still has a signficant economy. It exports more than a third of the world's supply of cocoa and has a small but promising oil production sector.
Several international leaders, including UN Secretary General Ban Ki-moon, have also warned that Gbagbo's decision to cling on to power could plunge Cote d"Ivoire back into civil war.
Meanwhile, the UN High Commissioner for Refugees says 14,000 Ivorians have feld to neighbouring Liberia amid the post-election violence.