* Yemen government awaits U.N. timetable for peace moves
* U.N. says Houthi forces withdrawn from Red Sea ports
* Four-year war has left millions facing hunger
ADEN, Yemen, May 12 (Reuters) - Yemen's government wants the United Nations to give time-frames for next steps of a peace deal after Houthi forces began withdrawing from key ports in the most significant advance yet for efforts to end the four-year war and relieve hunger.
In line with an accord in Sweden last year, the Iran-aligned Houthi movement began on Saturday a unilateral pullout from three Red Sea ports used for grain, oil, commerce and aid.
Local coast guards have taken over security at the Saleef, Ras Isa and Hodeidah ports, according to the United Nations which is supervising operations there.
Some officials from the Saudi-backed, internationally recognised Yemeni government dismissed the pullout as a "show", but government negotiator Sadiq Dweid acknowledged it marked the start of implementing the Stockholm accord.
The war has killed tens of thousands of people and left millions on the brink of famine.
Dweid tweeted late on Saturday that he had held a positive meeting with the chief U.N. observer, agreeing that the pullout should lead to time frames for implementing a U.N. mechanism for inspecting ships, de-mining and removing military installations.
While the Houthi move encouraged foreign powers pushing to re-open humanitarian corridors, displaced Hodeidah residents said they were not ready to return.
"We fled the war and I do not want to go back unless it ends, I fear death," said Sami, an 11-year-old who lives with his family in a graveyard in the capital Aden.
"War destroyed everything - no work and no security," said Abdul Rahman Taher, a 34-year-old man forced from his home in Hodeidah and now washing cars in Aden.
RETREAT FROM HODEIDAH
Saudi Arabia and the United Arab Emirates, leaders of the coalition backing President Abd Rabbu Mansour Hadi's government, have so far not commented on the Houthi ports withdrawal.
Sources saw this as a sign U.N. envoy Martin Griffiths had managed to get the warring sides to agree to the plan, since the coalition had quickly rejected a previous attempt by the Houthis to unilaterally withdraw last December.
Under plans to avert a full-scale assault, the Houthis are to pull back five km (three miles) from the ports between May 11 and 14. Coalition forces, currently massed four km from Hodeidah port on the edges of the city, are to retreat one km from two flashpoint districts.
In a second phase, both sides would pull troops 18 km outside the city and move heavy weapons 30 km away.
Aid organisation the International Rescue Committee said the Houthi move was a positive step, but a wider peace deal was needed to avert violence elsewhere.
"Among our biggest concern is ensuring sustained access to Hodeidah port," the Norwegian Refugee Council's Sultana Begum told Reuters. "Further military escalation risks cutting the supply line of vital food, fuel and medicines."
Hodeidah became the focus of the war last year when the coalition twice tried to seize its port to cut off the main supply line for the Houthis, whom they accuse of smuggling Iranian weapons, including missiles that have targeted Saudi cities. The group and Tehran deny the accusations.
(Reporting by Mohammed Ghobari in Cairo, Aziz El Yaakoubi and Lisa Barrington in Dubai Editing by Andrew Cawthorne)
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