During his meeting with Yemen's new Foreign Minister Khaled Alyemany, Mr Guterres stressed that "everyone should redouble efforts to find a political solution and avoid a fierce, bloody battle for Al Hodeidah", UN spokesman Stephane Dujarric said.
A broader United Nations peace plan calls on the Houthis to give up their missiles in return for an end to a coalition bombing campaign and a transitional governance deal, according to a draft document and sources.
U.N. Yemen envoy Martin Griffiths has urged the Houthis to hand over Hodeidah to U.N. control, Reuters reported on Sunday.
Yemeni security officials say gunmen shot dead a pro-government army colonel in the southwestern city of Taiz.
United Nations humanitarian chief Mark Lowcock told reporters after briefing the Security Council behind closed doors later Monday that it's critical to prevent "a battle" for Hodeida, which is a vital link for supplying millions of Yemenis with the necessities of life.
Residents on the west coast launched a campaign to remove Houthi slogans, he also said, hinting that the Hodeidah Port has become a spot to smuggle weapons to the Houthis.
Mark Lowcock, the head of the UN's office for the Coordination of Humanitarian Affairs, said the consequences of the suspension of operations at the port of Hudeida would be "catastrophic".
Britain has urged the UAE not to press ahead with an assault on Yemen's main port following United Nations warnings that the attack could leave hundreds of thousands dead in a country already on the brink of starvation.
"As much as 5,750,000,000 Yemeni Riyals equivalent to more than $22 million as well as 5,297 counterfeited passports were confiscated as they were being sent to the Houthi militias in Saada", Col.
UN Secretary General Antonio Guterres said there were "intense negotiations" by Griffiths with Yemen's rebel Houthis, Saudi Arabia and the United Arab Emirates to find a "way to avoid the military confrontation in Hodeida".
The Saudi-led coalition faces widespread global criticism for its air attacks in Yemen that have killed many civilians. The United States is also providing support to the coalition, including air-to-air refuelling and intelligence sharing.
US Secretary of State Mike Pompeo on Monday called on all parties "to honour their commitments to work with the UN". "In a prolonged worst case, we fear that as many as 250,000 people may lose everything - even their lives".
The Red Sea port is a lifeline for millions of people, handling most of the country's commercial imports and humanitarian aid supplies.