Guterres said his envoy Martin Griffiths was locked in "intense negotiations" with Yemen's rebel Huthis, Saudi Arabia and the United Arab Emirates to find a "way to avoid the military confrontation in Hodeida".
The three-year stalemated war has killed more than 10,000 people and displaced more than 3 million. "I hope that it will be possible to avoid a battle for Hudeida", Guterres said.
Correspondence sent from European donor governments to aid groups in Yemen on Saturday warned that "a military assault now looks imminent", according to the text of the correspondence seen by Reuters. "We have dozens of United Nations staff still in Hodeidah", Lowcock added.
Three civilians have been killed when a Houthi missile fired from Yemen hit the town of Jizan, in southern Saudi Arabia.
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The United Nations mobilized Monday to avert a "fierce, bloody battle" for a key port in Yemen that provides a lifeline for food, medicine and other vital supplies.
Previous UN efforts have failed to end the war.
"We expect all parties to honor their commitments to work with the UN Office of the Special Envoy of the Secretary General for Yemen on this issue, support a political process to resolve this conflict, ensure humanitarian access to the Yemeni people, and map a stable political future for Yemen".
"Our message is clear. if this assault happens then it would be very hard to imagine how hard the situation the people in Yemen, particularly in Hodeidah, will be in", said Muhsin Siddiqui, country director of Oxfam.
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On Tuesday, the Royal Saudi Air Defense Forces (RSADF) reportedly intercepted a ballistic missile launched by Iran-backed Houthi movement from Yemen targeting the Saudi territory. The U.S., he said, is closely following developments in Hodeidah and urged Emirati leaders to preserve "the free flow of humanitarian aid and life-saving commercial imports".
By late today, key lawmakers had begun losing faith in United States efforts to convince Saudi and UAE military officials to stop the assault, after The Wall Street Journal reported that the UN's shuttle diplomacy failed to move UAE officials and that the Donald Trump administration had given the operation "a blinking yellow light".
He also announced that humanitarian shipment permits were being granted regularly, and that humanitarian aid has been flowing continuously into all parts of Yemen.
Since 2015, Saudi Arabia has been leading a military campaign to push back the Houthis and restore the internationally recognized government to power.
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He cited the possibility that the United States could potentially do more on humanitarian relief, if asked, but said "right now we have not been asked to do more than what we're already doing".