A USA -backed, Saudi-led military coalition is fighting against the Houthis on behalf of the government of President Abd Rabu Mansour Hadi, who lives in exile in Riyadh.
Saudi sources said the United Nations special envoy for Yemen, Martin Griffiths, was in the Houthi-controlled capital, Sanaa, to discuss the possibility of worldwide control of the port, according to the Guardian.
Britain requested the urgent talks after telling aid agencies on the ground that it had received a warning from the United Arab Emirates that an attack was imminent.
Col. Turki Al Malki, the Official Spokesman of the Coalition to Restore Legitimacy in Yemen, stated that on Saturday, the Southern Region Operations Center announced that the terrorist Iranian-backed Houthi militia has targeted civilians with a projectile, which resulted in the martyrdom of three civilians in Jazan Governorate, the official Saudi Press Agency, SPA, reported.
The city is split between government and rebel control. The fighting has escalated as government forces close in on the Red Sea port city of Hodeida - a vital lifeline through which most of Yemen's food and medicine enters.
"We are, at the present moment, in intense consultation", the UN's secretary general, António Guterres, told reporters.
He said in a statement that he had spoken with leaders of the United Arab Emirates and "made clear our desire to address their security concerns while preserving the free flow of humanitarian aid and life-saving commercial imports".
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A military attack or siege on the Houthi-held western city, long a target in the war, could cost up to 250,000 lives, a senior United Nations humanitarian official has warned.
United Nations aid chief Mark Lowcock, who also briefed the council, said an attack on Hodeida would be "catastrophic" and that aid agencies were hoping to "stay and deliver" in Yemen, which the United Nations describes as the world's worst humanitarian crisis.
Eleven humanitarian aid agencies including Oxfam and Save the Children separately wrote to British Foreign Secretary Boris Johnson urging him to warn the coalition that it will lose British support if it attacks Hodeida.
But he urged them to support United Nations peace efforts.
The three-year stalemated war has killed more than 10,000 people and displaced more than 3 million.
Government forces, backed by a Saudi-led coalition, have been advancing along the western coast in recent weeks as they battle the Iran-allied rebels, known as Houthis. It has damaged Yemen's infrastructure, crippled its health system and pushed the Arab world's poorest country to the brink of starvation.