Obeidi, the new Libyan foreign minister who arrived in Cyprus on Wednesday for consultations with Kyprianou, did not make any comment to media as he left after the one-hour meeting.
Kyprianou told reporters that Obeidi focused on the African Union initiative and expressed the wish for a political solution.
He added they did not discuss whether Libyan leader Muammar Gaddafi would be ready to step down, a key demand of the rebels.
"We did discuss ideas, we put forward some suggestions on the table which the Libyan side will study. I think they will help but I can not mention the content until they are discussed," said Kyprianou, noting that the Cypriot proposals have taken into consideration the EU positions.
He also said Nicosia encourages the efforts based on the African Union-initiated peace roadmap, while underlining the need for an immediate ceasefire in order to protect civilians as required by relevant UN S1Security Council solutions.
Kyprianou said the international community should continue its efforts for a solution through dialogue, which should meet the expectations of Libyan people, though the recent AU initiative to broker a cease fire in Libya has been rejected by the rebels,
Obeidi visited Greece, Turkey and Malta earlier this month, seeking support from Libya`s Mediterranean neighbors.
The Cyprus government has expressed its opposition to the use of British military bases on the island for military intervention in Libya. (*)