The president of the EU council of member states, Herman van Rompuy, and European Commission President Jose Manuel Barroso, said dialogue between all elements of Libyan society was needed for a successful transition to democracy.
"The reported death of Muammar Gaddafi marks the end of an era of despotism and repression from which the Libyan people have suffered for too long," they said in a statement.
"We call on the National Transitional Council to pursue a broad-based reconciliation process which reaches out to all Libyans and enables a democratic, peaceful and transparent transition."
Several NTC officials said Gaddafi was killed during a fight for his hometown in Sirte on Thursday. But Western powers, who have backed the rebellion which took the capital Tripoli two months ago, said they were still seeking confirmation.
"If confirmed, his death brings closure to a tragic period in the lives of so many Libyans," the EU`s foreign policy chief, Catherine Ashton, said in a statement.
Ashton said European governments would continue to support the NTC in its efforts to reconstruct Libya after eight months of fighting that has displaced hundreds of thousands of people.
"We have already supported civil society and we are now working with international partners to respond to Libya`s post-conflict needs," she said in the statement. "The EU will remain a strong and committed partner in the future."
Last month, during an international conference on Libya, EU states agreed to focus their reconstruction assistance on border management, strengthening civil society and women`s rights, and media and communications.
"It is important that its leadership unites to build a democratic future for the country in full respect for human rights. While the crimes of the past must be addressed, the leadership must also seek a path of national reconciliation," Ashton said.
The EU has provided more than 150 million euros ($205 million) so far in humanitarian assistance to Libya. (*)