(Adds location of talks in paragraph 4) By Patrick Worsnip UNITED NATIONS, June 4 (Reuters) - Ground-breaking talks to try to end a three-decade deadlock over the future of Western Sahara will take place on June 18-19 on Long Island, near New York City, U.N. officials said on Monday. The talks will group officials from Morocco, which annexed the former Spanish colony after Madrid pulled out in 1975, the territory's Polisario independence movement, Algeria, where Polisario is based, and neighboring Mauritania. Dutch diplomat Peter van Walsum, U.N. special envoy for the phosphate-rich territory in northwestern Africa, "will conduct direct or proximity talks as a first step in the process of negotiations," U.N. spokeswoman Marie Okabe said. The talks follow Morocco and the Polisario's agreement in April to negotiate. They will be held at a private estate in the town of Manhasset previously used for territorial negotiations between Nigeria and Cameroon, diplomats said. Morocco's annexation of Sahara, based on what Rabat said were centuries-old rights, triggered a low-level guerrilla war with the Polisario. A U.N. ceasefire agreement in 1991 promised a referendum on the territory's fate, but it never took place. Polisario still demands a referendum with independence as an option, but Rabat now says that is impossible because Sahrawis are scattered across Algeria, Mali, Mauritania and Morocco, and that autonomy is the most it will offer. One spur to negotiations has been that the United States is now impatient for a deal in hopes it will bring more cooperation between North African states and help combat terrorist groups in the regions bordering the Sahara. The Western Sahara dispute is the main cause of friction between Morocco and Algeria, whose land borders, closed in 1994 amid security tensions, remain shut. Morocco and the Polisario have met before but U.N. diplomats are billing this month's talks as the best hope yet for a settlement. "The impression we had ... is that both parties have well registered the message that they now have to grasp that opportunity to sit together in talks," said Belgium's U.N. Ambassador Johan Verbeke, current Security Council president. "So there is a lot of confidence among the members of the Security Council," Verbeke said on Monday. Polisario leader Mohamed Abdelaziz told Reuters in an interview last week, however, that failure at the talks to break the deadlock could destabilize North Africa and reignite his movement's armed struggle.