A US -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.
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.
The United Nations fears that a battle in Hodeidah could be devastating for the estimated 600,000 people still living in the city.
During the closed session, Griffiths was to brief council members by video-conference from Amman along with United Nations aid chief Mark Lowcock.
Guterres said U.N. Yemen envoy Martin Griffiths was shuttling between Sanaa and also the UAE and Saudi Arabia.
Worldwide aid group Doctors Without Borders said Monday the Saudi-led coalition attacked a cholera treatment center in the northern province of Hajja. I urge you to speak out publicly against the offensive and warn our allies that Congress will introduce legislation to end U.S. assistance for their campaign should they move ahead with an attack.
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As one of his first official acts as president, Trump pulled the United States out of the Trans-Pacific Partnership. Many countries have policies and trade barriers created to protect specific agricultural sectors.
Most countries have since withdrawn their forces from the coalition, with only Saudi Arabia and the United Arab Emirates conducting attacks in Yemen.
The letter comes after the United Nations and humanitarian groups reported over the weekend they were warned by the United Arab Emirates to evacuate Hodeida by Tuesday.
Griffiths previously said an attack on Hodeidah would "take peace off the table in a single stroke". "But we are also anxious about the humanitarian situation".
The war has killed more than 10,000 people, displaced three million and unleashed the world's most urgent humanitarian crisis in the impoverished Arab state which is struggling with a starvation and cholera epidemic, according to the United Nations.
The United States urged all parties of the conflict to ensure humanitarian access to the Yemeni people, Secretary of State Mike Pompeo said Monday.
Assistance provided by King Salman Center for Humanitarian Assistance and Relief Aid (KSRelief) as part of the comprehensive humanitarian operations in Yemen have until Monday benefited 4,791,792 Yemeni citizens, he said.