Nevertheless, he added, Sanaa's worldwide airport "remains open to United Nations and humanitarian aid deliveries".
Earlier in the day, Guterres had called for a halt to violence in Yemen to pull the country back from a "precipice" and build momentum toward talks on ending the war.
After UN-backed peace talks collapsed in September, the coalition announced it was relaunching an assault on Hodeida.
The alliance, which relies on Western arms and intelligence, was on Wednesday still sending troops to the Houthi-held port city of Hodeidah where it has massed thousands of forces in recent days, pro-coalition Yemeni military sources said.
Yemen has been at war since March 2015 when Houthi rebels occupied northern regions and forced the government into exile.
"We must do all we can to maximize the chances for success", Guterres further said, calling for commercial and humanitarian imports of food, fuel and other essentials to be allowed into Yemen without restrictions.
Pompeo also said the U.S. was also embarking on a new push for peace in Yemen, where as many as 50,000 have died and the country has been plunged into a major humanitarian crisis.
"My objective is to appeal to the parties to the conflict to understand that there is an opportunity that must be seized, and to say that the humanitarian situation is so dire that if that doesn't happen" the world will have to deal with a starvation in Yemen next year, he said.
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Following the collapse of the talks, which would have been the first of their kind in almost two years, the coalition announced it was relaunching an assault on Houthi-held Hodeidah, a strategically important Red Sea port city.
Over the past few months, the United States has said little about the war, which has led to one of the world's worst humanitarian crises.
The clashes came hours after the Saudi-UAE alliance said it had bombed Sanaa International Airport and an adjoining airbase.
The attack was the latest attempt by the Houthis in response to the Saudi-led airstrikes.
But the secretary-general stressed that the U.N.'s immediate priority is to stop the bombing in populated areas and preserve critical infrastructure including in the key port of Hodeida, the main entry point for worldwide aid and 70 percent of food imports that Yemen relies on.
The coalition has imposed a blockade on the port, however, allegedly as part of efforts to prevent the Houthis from using it as a landing point for weapons supplied by Iran.
The conflict in the Arab world's poorest country began with the 2014 takeover of Sanaa by the Houthis, which toppled the internationally recognized government.