Morocco and the Polisario independence movement concluded a second day of UN-brokered talks on Saturday and agreed to meet again for more negotiations.
The talks about their 32-year-long dispute over Western Sahara ended with no breakthroughs.
"The parties acknowledge that the current status quo is unacceptable and they have committed to continue these negotiations in good faith," read a UN statement signed by UN chief Ban Ki-moon's envoy for Western Sahara, Peter Van Walsum.
Negotiators have still to set a place and date for the next round of talks, Van Walsum said.
The talks, held in Manhasseet, just east of New York City, focused on the status of the north African territory.
Polisario wants a referendum offering full autonomy or independence, while Rabat has so far only been willing to offer limited autonomy under Moroccan sovereignty.
"I am pleased that we were able to hold substantive talks in which the parties interacted with one another and expressed their views," said Van Walsum.
"The parties heard presentations by United Nations experts on specific issues such as natural resources and local administration. Confidence-building measures were also proposed for discussions," he said.
The two sides held their first face-to-face talks in at least seven years in June.
Speaking to reporters after the meeting, Moroccan Interior Minister Chakib Benmoussa, who headed the Moroccan delegation, said his delegation's decision to accept a third round of talks had been influenced by approaching legislative elections in Morocco that are scheduled for September 7.
But Benmoussa said that "after two days of negotiations, the Kingdom of Morocco cannot but express its regret since the other party did not seize the opportunity offered by the second round with a view to making progress in our quest for a political solution to this conflict."
The Moroccan minister decried Polisario's position as "rigid," adding that the front was "clinging to plans and proposals that proved inapplicable."
Meanwhile, Radhi Bachir Seghaier, an adviser to Polisario leader Mohamed Abdelaziz, told Algerian APS news agency that the lack of progress should be blamed on Moroccan "intransigence."
"They have assumed an inflexible posture," Seghaier said of Moroccans, pointing out that Rabat "would not accept" any solution other than autonomy under Moroccan sovereignty.
However, Mahfoud Ali Beiba, head of the Polisario delegation, described the round of talks as "useful," arguing in a statement that it had ven the front an opportunity to present its proposals aimed at resolving "the decolonization conflict of Western Sahara."
Earlier this month, Moroccan King Mohammed VI warned against "Balkanization" on the African continent due to separatist movements.
Beiba, for his part, reasserted the organisation's aim to achieve full self-determination for Western Sahara and said negotiations would require "perseverance, patience and creativity."
Rabat annexed the northwest African territory on the Atlantic coast after former colonial ruler Spain and neighbouring Mauritania withdrew in the 1970s, sparking a 16-year long war with the Polisario Front.
The two sides reached a ceasefire in 1991, but Rabat repeatedly pushed back a promised self-determination referendum and since 2002 has insisted such a vote is not necessary.
In April, Morocco proposed an autonomy referendum that envisages giving Western Sahara control over its affairs through legislative, executive and judicial institutions but under Moroccan sovereignty.
Rabat also wants Algeria, the Polisario's main backer, to be involved in any settlement. Delegates from both Algeria and Mauritania were at Friday's talks.