Fighting was focused around the airport, which the coalition failed to seize in a previous offensive, and also at the eastern entrance to the city and near a university that lies 4 km south of the port, which handles most of Yemen's imports.
"Yemen is today a living hell - not for 50 to 60 percent of the children - it is a living hell for every boy and girl in Yemen", he told a news conference in the Jordanian capital.
Geert Cappelaere also told The Associated Press in an interview from Yemen that a US call for a cease-fire is imperative to end the "brutal war".
The UN chief spoke hours after the Saudi-led coalition said it had attacked an airbase in the capital, Sana'a, and fighting flared between the Houthis and the Saudi-led forces near the western port city of al-Hudaydah. He said the situation in Yemen now to his last visit in 2017 is deteriorating, adding that "the war is taking hostage millions of Yemenis who can't afford basic needs".
Two months before that, coalition air raids severely damaged an Oxfam-supported water supply system that provided water for 6,000 people.
UN refugee agency UNHCR special envoy Angelina Jolie said the global community had been "shamefully slow" and urged the UN Security Council to find a negotiated end to the war.
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The waivers are only temporary, and the USA will expect countries to keep cutting Iranian imports in the months ahead, it added. What's the point?Oil is big business in Iran, with exports accounting for more than a tenth of gross domestic product in 2017.
"UN member states must end their deafening silence on Saudi Arabia and do their duty of scrutinising the cruelty in the kingdom in order to prevent further outrageous human rights violations in the country and in Yemen", Samah Hadid, Amnesty International's Middle East director of campaigns, said in a statement. According to the world body, Yemen is suffering from the most severe starvation in more than 100 years.
"The only way to enable refugees to return home, and to bring down the overall numbers worldwide, is to end conflicts themselves".
The coalition has been working in Yemen since 2015 under Saudi command to reestablish in Sanaa the internationally recognized government of President Abd Rabbo Mansour Hadi, a refugee in Riyadh.
The latest fighting comes a day after the Yemeni government said it welcomed efforts to restore peace following calls by key United States officials and the UN's envoy to Yemen Martin Griffiths for warring parties to come to the table "within a month".
The secretary-general of the united Nations, Antonio Guterres had also called Friday to the end of the "violence" in order to avoid that the country does not fall into a "precipice".
They say Sunday that airstrikes and naval artillery have pounded rebel positions around the Red Sea costal city, which government backed-troops launching a major ground assault seek to wrest from dug-in rebels.