"I hope that there will be a way to avoid the military confrontation in Hodeida", Guterres told reporters.
Yemeni security officials say gunmen shot dead a pro-government army colonel in the southwestern city of Taiz.
Amid new clashes in Yemen, the United States on Monday called on factions to work with the United Nations to end the more than three-year-old conflict that has pitted Iran-aligned Houthis against other Yemeni forces backed by a Saudi-led coalition.
Houthi rebels in Yemen have ramped up missile attacks on Saudi Arabia in recent weeks and months.
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".
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 UN has already dubbed Yemen the world's worst humanitarian disaster.
Al Hodeidah, the country's second-largest port, also provides a lifeline for food, medicine and other vital supplies.
Meanwhile, the U.S. was following developments in Yemen very closely, said Secretary of State Mike Pompeo.
Eleven humanitarian aid agencies, including Oxfam and Save the Children, separately wrote to British Foreign Secretary Boris Johnson urging him to warn the coalition that it will lose British support if it attacks Hodeidah.
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.
Since 2015, Saudi Arabia has been leading a military campaign to push back the Houthis and restore the internationally recognized government to power. It has damaged Yemen's infrastructure, crippled its health system and pushed the Arab world's poorest country to the brink of starvation.