Yemen's government wants the U.N. to give time frames for the 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 U.N., which is supervising operations there.

Some officials from the Saudi-backed, internationally recognized Yemeni government dismissed the pullout as a "show."

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 Saudi 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. 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.

The ongoing war has resulted in the worst humanitarian crisis in the world, with an estimated 24 million people, close to 80 percent of the population, in need of assistance and protection in Yemen, according to the U.N. The World Health Organization (WHO) says some 10,000 people have been killed since the coalition intervened in 2015, but rights groups state the death toll could be five times as high. Saudi-led attacks have killed nearly 4,600 out of the 7,000 verified civilians who have died in the war, according to recent figures by the U.N. Human Rights Office.