The conflict escalated in 2015 when Saudi Arabia and its Sunni-Arab allies - who accuse the Houthis of serving as Iranian proxies - launched a massive air campaign in Yemen aimed at rolling back Houthi gains.
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.
Hudaida lies some 230km away from the capital, Sanaa, which is controlled by the Houthis.
After briefing the Security Council on Monday, U.N. aid chief Mark Lowcock told reporters that "if for any period Hodeidah were not to operate effectively the consequences in humanitarian terms would be catastrophic".
Houthi rebels in Yemen have ramped up missile attacks on Saudi Arabia in recent weeks and months.
Al-Maliki said residents have welcomed the advancing government forces through such gestures like removing sectarian graffiti from walls of liberated towns and cities in Saada as well as the port of Hodeidah.
The Saudi-led coalition faces widespread worldwide criticism for its air attacks in Yemen that have killed many civilians.
United Nations aid chief Mark Lowcock, who also briefed the council, said an attack on Hodeidah 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.
"While the United Nations and other humanitarian agencies are reconfiguring their presence it's also our planned intention though to stay and deliver".
He said past and present United Nations efforts had been met with "intransigence" by the Houthis who he said have refused a political solution to end the crisis.
The United States urged all parties of the conflict to ensure humanitarian access to the Yemeni people, Secretary of State Mike Pompeo said Monday.
Hodeidah handled 90 percent of the nation's foodstuffs and the humanitarian aid flow before the war, and periodic Saudi blockades of the port since 2015 have heightened fears of starvation and compounded aid agencies' response to a deadly cholera outbreak a year ago.
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".