Speaking on Thursday, about the new round of talks, Zalmay Khalilzad, US ambassador to the UN, said: "We hope they will get to substantive issues and that there will be further progress."
However, UN officials said the most likely outcome from the two day meeting at the secluded Greentree Estate in Manhasset, about 40km east of New York city, is agreement on another meeting, or a series of meetings.
Morocco and the Polisario Front agreed to meet after the UN Security Council unanimously adopted a resolution on April 30 urging talks over the region.
The talks are being held under the auspices of Peter Van Walsum, personal envoy for Ban Ki-moon, the UN secretary general, for Western Sahara.
1884 - Spain colonises Western Sahara.
1957 - Morocco raises claim to Western Sahara at the UN.
1973 - Polisario formed to wrest Western Sahara from Spanish control and establish an independent Saharan state.
Mid-1975 - Morocco takes territorial dispute to the World Court. Rules that issue should be settled through self-determination.
Late-1975 - Spain withdraws from Western Sahara and Morocco and Mauritania split the territory.
1976 - Polisario relocates to Algeria, proclaims the Saharan Arab Democratic Republic (SADR) with a government-in-exile, launches full-scale war on both Mauritania and Morocco.
1979 - Mauritania signs peace deal with Polisario and withdraws from Western Sahara. Morocco annexes the whole territory.
1984 - SADR is admitted to the Organisation of African Unity. Morocco leaves in protest.
1991 - UN brokers cease-fire between Morocco and Polisario with an agreed referendum for the region.
1992 - Referendum postponed because of dispute over who is eligible to vote.
2003 - UN proposes Western Sahara becomes a semi-autonomous region of Morocco for up to five years, to be followed by a referendum. Polisario endorses the plan but Morocco rejects it.
Mid-2007 - Polisario and Moroccan government hold first direct negotiations in seven years.
Morocco, which annexed the former Spanish colony in 1975 sparking a 16-year war with the Polisario, has insisted that its autonomy plan, unveiled in early April, offers "the only realistic solution".
The Polisario Front, an indigenous independence movement backed by Algeria, maintains that its April proposal for a referendum with independence as an option is crucial to achieving self-determination for the people of Western Sahara, and to complete the territory's decolonisation.
Armed conflict between the Polisario's 15,000 fighters and Morocco's US-equipped army ended in 1991 with a UN-negotiated cease-fire that called for a referendum on the region's future.
But after 15 years and the expenditure of more than $600m, the UN has been unable to resolve the standoff or hold the referendum.
James Baker, former US secretary of state, organised talks on behalf of the UN in 1997 and again in May 2000 to try to salvage plans for an independence referendum, but no progress was made because Morocco and Polisario did not agree on voter lists.
A UN peace plan in 2003, which envisioned temporary autonomy followed by a referendum in which both Saharan and Moroccan settlers would vote, was accepted by Polisario but rejected by Morocco.
Hopes for peace
Ahmed Boukhari, the Polisario's UN representative, said on Thursday that if Morocco respects the Security Council resolution and treats the proposals presented by the two parties equally, then "there will be hopes for the peace process engaged in Manhasset, and this round will be positive for that process".
"However, taking account of the latest statement by Morocco officials, we have no assurance nor hopes that Morocco is going to respect the terms of the resolution, and it is going to threaten the peace process like they destroyed Mr. James Baker's efforts in 2003."
At the end of June's negotiations, Khalihenna Ould Errachid, the chief adviser on Western Sahara to King Mohamed VI of Morocco, said there was a need for compromise and "a renunciation to extremist positions and demands".
"Morocco has given up total integration and we expect the other party to give up total independence."
Last month, the US backed Morocco's offer of regional autonomy but other UN Security Council members said independence must remain an option.