Military officials said Saudi-led coalition warplanes carried out dozens of air strikes to support pro-government forces in the fighting which began on Thursday evening.
The Houthi official responsible for foreign affairs, Hisham Sharaf, praised Griffiths' continued efforts, but urged Western governments to take concrete steps to enforce a ceasefire to create "conditions conducive to peace far away from any pressure or dictates", the Houthi-run Saba news agency said.
Geert Cappelaere, regional director for the Middle East and North Africa at the United Nations children's agency UNICEF, called on the warring parties to join proposed peace talks later this month and agree to a ceasefire.
The bloodshed comes despite growing global pressure to end a years-long conflict that has killed thousands and pushed the impoverished Arabian Peninsula nation to the brink of starvation.
"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.
Three-quarters of Yemen's 29 million people are food insecure, 1.8 million children suffer from malnutrition and 400,000 children under age 5 are at risk of death from starvation.
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British foreign secretary Jeremy Hunt will announce on Monday that the United Kingdom is discussing with UN Security Council partners what more the Council can do to address the humanitarian crisis in Yemen and step up support for the work of the UN special envoy Martin Griffiths.
The impoverished Arab country has been locked into a civil war since the Iran-backed Shiite Houthi rebels overran much of the country militarily and seized all northern provinces, including the capital Sanaa, in 2014.
The rebels, known as Houthis, said they repelled the latest offensive on Hodeida, killing or wounding 215 troops, but did not provide a breakdown.
"This is the first time clashes have reached this point (the university)", one pro-coalition Yemeni military source said.
Yemen's internationally recognised government On Thursday welcomed a call from the USA for peace in the conflict-torn country, state-run news agency Saba said.
The coalition has deployed thousands of troops to retake Hodeida, a vital entry point for imports and a lifeline for millions of Yemenis after more than three years of war.
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The United States and Britain have called for an end to the conflict, raising pressure on Saudi Arabia as it faces a global outcry over the murder of prominent Saudi journalist Jamal Khashoggi in the Saudi consulate in Istanbul on October 2.
According to the World Health Organization, almost 10,000 people have been killed in the conflict, though some rights groups estimate the toll could be five times higher.
After UN-backed peace talks collapsed in September, the coalition announced it was re-launching an assault on Hodeida.
Saudi Arabia and its allies intervened in the war in the following year to bolster Yemeni President Abedrabbo Mansour Hadi whose government fled to the southern city of Aden.
According to the World Health Organisation, almost 10,000 people have been killed in the conflict since 2015.
UN Secretary-General Antonio Guterres on Friday had called for a halt to violence to pull Yemen back from the "precipice".
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A few seconds into the video, a woman is hitting the bus driver on his head with a phone. The driver then took his right arm off the steering wheel as he tried to defend himself.