In a major breakthrough, Greek and Turkish Cypriot leaders agreed Friday to resume full negotiations next week to end the 30-year division of Cyprus (search) before it joins the European Union on May 1.

The agreement caps a lengthy and often tortuous effort by Secretary-General Kofi Annan to end one of the world's longest and most intractable disputes. It came after three days of grueling talks, including a marathon session that dragged on into the early hours Friday among the Greek and Turkish Cypriot leaders as well as Greek and Turkish diplomats.

Under the deal brokered by Annan, negotiations will resume Feb. 19 in Cyprus. If the Greek and Turkish sides fail to reach an agreement, Annan will decide any outstanding issues — but Greek and Turkish Cypriots will have the final say on the agreement in referendums in April.

"We have not yet solved the problem," Annan cautioned, "but I really believe that after 40 years, a political settlement is at least in reach, provided both sides summon the necessary political will."

When the last round of talks collapsed in April 2003, Annan said he would not get involved unless the sides showed political will to end the island's division. With international pressure mounting for a united Cyprus to join the EU and signs that the Greek and Turkish Cypriots were willing, Annan invited the parties to New York.

After three days of difficult talks, capped by Thursday's 12-hour session that diplomats said dissected almost every word of a 1-page statement on resuming negotiations, there was one major outstanding issue — the Greek side's demand that the EU take part in the talks. Turkey was against it.

Britain, the former colonial power in Cyprus, and the United States used intense diplomacy to pressure both sides to accept the agreement. U.S. envoys spoke to the foreign ministers of Greece and Turkey, and Secretary of State Colin Powell and British Foreign Secretary Jack Straw called Greek Foreign Minister George Papandreou, U.N. diplomats said.

In the end, Annan decided that the issue was minor and he made a take-it-or-leave-it final proposal that welcomed EU assistance — but didn't give the European body a role in the talks. It was sent to Turkish Cypriot leader Rauf Denktash (search) and Greek Cypriot President Tassos Papadopoulos (search) on Friday, and they agreed.

"This is the beginning of the process," Denktash said. "The most important thing is for us to continue this process in such a way that we will be able to protect the rights of our people."

"There have been so many false hopes in the past," Papadopoulos said. "I wouldn't like to make a prediction. I hope this will be solved."

In Washington, State Department spokesman Richard Boucher said, "We're pleased that the parties are seizing this historic opportunity to achieve a just and durable settlement to the longstanding division of Cyprus."

Foreign Secretary Straw congratulated the parties to the agreement.

"I express my special appreciation of the U.N. secretary-general," Straw said. "Accession to the EU by a reunited island is what all Cypriots deserve."

Cyprus was divided in 1974 after a coup and Turkish invasion into a Turkish-occupied north and a Greek-controlled south. If the island is still divided on May 1, the EU laws and benefits will apply only to people in the Greek Cypriot south.

The negotiations will focus on a U.N. blueprint for reunification that calls for a single state with Greek and Turkish Cypriot federal regions linked through a weak central government.

The last round of talks collapsed when Denktash rejected Annan's plan, primarily because it provided for the return of half the 200,000 Greek Cypriot refugees to Turkish-occupied territory in the north.

The agreement calls for Greek and Turkish Cypriots to try to finalize a plan on reunifying Cyprus by March 22. If that fails, Annan would bring Turkey and Greece into the talks to try to resolve the issue by March 29.

As "a final resort," Annan would submit his own plan for a referendum.

Turkey has been pressing a Cyprus solution ahead of the opening of its membership negotiations with the EU later this year. EU leaders say failure to resolve Cyprus could complicate Turkey's own bid to join the 15-member European bloc.

Turkey Foreign Minister Abdullah Gul expressed hope "that everything is resolved by May 1," saying reunification "will be a symbol of peace, stability, development, and cooperation in the region."

"That's our wish and that's what we're working for," he said in Ankara. "Of course this doesn't mean it will be easy. Certainly after the negotiations begin, it will be difficult ... patience and good will be needed."

Annan's special envoy Alvaro de Soto, who will mediate the Cyprus talks, was optimistic.

"We have the impression that this time there is a different mindset and that negotiations should work much better than what transpired during the previous 3 years," he said. "I have a good feeling about this."