"In a prolonged worst case, we fear that as many as 250,000 people may lose everything, even their lives", added the United Nations official.
Humanitarian agencies working in Yemen remain deeply anxious about the likely impact of a Saudi-led assault, since as many as 600,000 civilians now live in and around Hudaydah, which lies on the country's Red Sea coast.
The UN warned that the likely "catastrophic humanitarian impact" would be worsened due to Hudaida's key role as the point of entry for some 70 percent of Yemen's imports. "My aim is to restart negotiations which have not taken place for a very long time, for too long, and I want that to restart in the very near future", he said.
Twenty Houthi rebels were killed in clashes with Yemen's military in central Marib province, military officials said Thursday. The ICRC statement did not identify the source of the threats.
There was no immediate comment from the Houthis regarding the army's claims.
The conflict pits the Iran-aligned Houthis, who took control of the capital Sanaa in 2014, against other Yemeni forces backed by a coalition loyal to exiled President Abd-Rabbu Mansour Hadi and led by USA allies Saudi Arabia and the United Arab Emirates.
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It started with the tariffs on steel and aluminum that were imposed on Canada and other G7 nations by Donald Trump . If the dispute can't be resolved, the two countries can take the matter to the World Trade Organisation, she said.
Saudi Arabia, the United Arab Emirates and Sunni Muslim allies entered the war in 2015 to try to drive back the Houthis, an Iran-allied Shi'ite movement that forced a Saudi-backed government into exile in 2014.
Previous efforts to end the conflict, which according to the United Nations has killed more than 10,000 people, have failed.
Yemen's humanitarian crisis is considered the worst in the world.
About 450 ICRC workers remain in Yemen, but ICRC spokeswoman Marie-Claire Feghali said the organization could pull out additional employees in the coming days if security threats continue.
Those withdrawn from Yemen represent more than half of the ICRC's global staff in the country and one fifth of its total staff, spokeswoman Marie Claire Feghali told AFP.