BRUSSELS, July 6 (Reuter) - The EU and Morocco emerged in optimistic mood from a fresh round of talks on Thursday aimed at ending a drawn-out dispute over a new fisheries agreement.

EU fisheries commissioner Emma Bonino said she was more optimistic that a new agreement could be reached.

"It was a positive meeting...I am more optimistic," she told reporters after 40-minute talks with Moroccan Prime Minister Abdellatif Filali.

"I think the visit was very positive. It allowed us to open up a friendly and realistic dialogue about the problems which face us," Filali told reporters after meeting Bonino andother EU commissioners.

Bonino said officials would continue talks over dinner and she hoped they would fix a date for a sixth round of negotiations.

"We reviewed different pieces of the puzzle but some are still missing," she said adding that she hoped to see the remaining pieces in place later this evening.

Filali, who had been expected to put forward fresh proposals, said he would "possibly" return to Brussels next week for fresh talks after today's session had clarified the situation.

The EU and Morocco have been at loggerheads over Moroccan demands for sharp cuts in quotas and increased landings of catches in Moroccan ports.

The agreement with Morocco is the EU's most important external fisheries agreement providing a livelihood for 28,000 people in southern Spain, the Canary Islands and Portugal.

Under the previous agreement. which expired at the end of April, Morocco earned $130 million a year for fishing rights.

Talks on fisheries and on closer political links between Morocco and the European Union have become entangled in recent months, a situation both sides said they wanted to resolve.

"The two sides have agreed to relaunch negotiations, both on the fisheries agreement and Morocco's association agreement with the European Union," a European Commission spokesman told reporters after formal talks ended.

The spokesman said Commission President Jacques Santer and Filali had pledged to keep the issues apart.

"(Santer) strongly insisted that these two issues should be negotiated according to their own merits, that is to say separately," the spokesman said.