Zeid Ra'ad al-Hussein said on Monday: "I emphasise my grave worry regarding the Saudi and Emirati-led coalition's ongoing attacks in Hudaida - which could result in enormous civilian casualties and have a disastrous impact on life-saving humanitarian aid to millions of people which comes through the port."
Saudi Arabia and United Arab Emirates, despite superior weaponry and firepower, have failed to defeat the Yemeni people in a war that has killed 10,000 people and created the world's most urgent humanitarian crisis.
The battle for Hudaida, launched six days ago, could drag on, inflicting more suffering on civilians who have already endured air raids, port blockades, hunger and a cholera epidemic.
Meanwhile, Stephane Dujarric, the spokesperson for UN Secretary-General, Antonio Guterres , told reporters on Monday that about 5,200 families, or around 26,000 people, have sought safety within their own districts or in other parts of Hudaida governorate.
Dujarric added: "The number is expected to increase as hostilities continue."
Also, The UN envoy for Yemen has arrived in Sanaa for crisis talks on the port city of Hudaida amid growing fears that fighting between a Saudi and Emirati-led coalition and Houthis will exacerbate a humanitarian crisis.
Martin Griffiths did not make any statement as he landed in the Yemeni capital on Saturday.
Griffiths's arrival came as fighting intensified around Hudaida's airport amid conflicting claims over its fate.