A joint statement by the two Gulf states called on the UAE-backed separatists and the Saudi-backed government to prepare for "constructive dialogue" to end the crisis between the two nominal allies.
Saudi Arabia and the United Arab Emirates called on Yemen's separatists and the internationally-recognised government of President Abd Rabbu Mansour Hadi to halt all military actions in south Yemen.
A joint statement by the two Gulf states, leaders of an Arab coalition that is battling Yemen's Iran-aligned Houthis, called on the UAE-backed separatists and the Saudi-backed government to prepare for "constructive dialogue" to end the crisis between the two nominal allies.
Talks to end the power struggle, in the Red Sea city of Jeddah, reached a dead-end and both sides were gathering troops to prepare for further battle, officials said on Friday, an indication that a rift between Saudi Arabia and ally UAE had deepened.
The war for the south has opened a new battlefront that risks further fragmenting Yemen and threatens to complicate UN efforts to end the multi-tiered war, which contains conflicts within conflicts.
"They (the two countries) also called for an immediate end to all military operations as well as violations against any public and private property," the joint statement carried by state news agencies SPA and WAM, said.
"They have been preparing for a constructive dialogue to end the dispute and address its effects," it added.
The breakaway movement is part of the Saudi-led coalition that intervened in Yemen in March 2015 to restore Hadi's government which was ousted from power by the Houthis in the capital Sanaa in late 2014.
But they have clashed often with the government and seized Aden, its interim base, last month.
The UAE intervened last week to support the separatists by launching air strikes on government forces as they tried to recapture Aden, forcing them to withdraw.
Saudi Arabia called on the separatists, who seek to revive the former South Yemen republic, to cede control of Aden and voiced its support for President Hadi on Thursday, threatening "to react decisively".
However, Sunday's statement said the two Gulf states reiterated their support of Yemen's "legitimate government".