The arrival of the CMA CGM Cortes ship followed that of the CMA CGM Rabat, which has since left Abidjan, a spokeswoman for the group said.
Freight operators have been expecting export activity from Ivory Coast to resume this week after being halted by a political crisis in the West African state.
Safmarine said it was loading its first cocoa exports from the country since the end of an export ban.
CMA CGM has said all its ships are equipped to handle cocoa but has so far declined to comment on what cargo the vessels have carried.
The arrest recently of incumbent leader Laurent Gbagbo has opened the way for the resumption of shipping, with the lifting of European Union sanctions and of an export ban called by Alassane Ouattara, the rival leader who was widely seen as the winner of recent elections.
Shippers have said that a full resumption of cocoa exports from Ivory Coast could take weeks.
The Rosa Delmas ship, which had been due to be company's second arrival in Abidjan on Wednesday, did not call at the port, the spokeswoman said, declining to comment on the reasons. (Reuters)
