The Security Council on Thursday gave strong backing to efforts by U.N. Special Envoy Martin Griffiths to start new talks between Yemen's warring parties.
The council issued a statement, following a closed-door briefing by Griffiths, reaffirming that "a political solution remains the only way to end the conflict."
Council members said they "encouraged all parties to engage constructively with his efforts to take forward a political solution."
However, Al Arabiya reported that Houthi rebels had rejected Mr Griffiths' latest proposals to hand over the port of Hodeidah and restart peace talks, instead suggesting the UN manage the facility under their supervision.
The rebels took over Yemen's capital Sanaa in 2014 and routed the internationally recognized government. A Saudi-led coalition allied with the government has been at war with the Houthis, who are backed by Iran, since 2015.
Previous peace efforts have failed but Griffiths, who was appointed to the post in February, expressed optimism in a statement Wednesday after meeting top Houthi leaders in Sanaa.
Griffiths said without elaborating that the rebels and their allies have expressed a "strong desire for peace" and discussed "concrete ideas for achieving peace." But a Houthi negotiator said there was no breakthrough in negotiations.
The United Arab Emirates, a major pillar in the Saudi coalition, has been leading a battle to retake the key Red Sea port town of Hodeida from the Houthis. But it put the campaign on hold to give the U.N. envoy a chance to broker a peaceful solution.
The Security Council reiterated its call for Hodeida and the port of Saleef "to be kept open and operating safely given the continuing risk to the grave humanitarian situation."
The U.N. hopes to prevent a full-scale coalition assault on Hodeida, which is responsible for more than 70 per cent of imports to Yemen and is a vital lifeline for a country already teetering on the brink of famine.
More than 10,000 people have been killed in Yemen's civil war, which has displaced 2 million people, helped spawn a cholera epidemic, and created the world's worst humanitarian crisis, according to what the United Nations.