The assault marks the first time the Arab states have tried to capture such a heavily-defended major city since they joined the war three years ago against the Iran-aligned Houthis, who control the capital Sanaa and most of the populated areas.
Charities have warned the targeting of Hodeida will begin an intractable and bloody new chapter in the conflict, trapping civilians and prompting the closure of the port to make starvation a "very real possibility". Houthi forces have fired missiles at ships previously.
UAE Minister of State for Foreign Affairs Anwar Gargash told the Houthis on Tuesday that the "final hour" is approaching in Hodeidah.
UAE-backed Yemeni forces - drawn from southern separatists, local units from the Red Sea costal plain and a battalion led by a nephew of late former President Alo Abdullah Saleh - are fighting alongside Emirati and Sudanese troops. Saudi Arabia, the UAE and other members of the coalition have fought to restore the ousted government and roll back Iran's influence in the region.
Al Hodeidah, the second largest port in the country, is the main conduit for humanitarian supplies into a country teetering on the brink of starvation.
The United Nations and other aid groups already had pulled their worldwide staff from Hodeidah before the rumoured assault.
Planes and warships began pounding Houthi rebel fortifications and forces massed around Hodeida on Wednesday as a deadline for Houthis to leave the city passed.
Over 10,000 people have been killed in Yemen's civil war, which has displaced 2 million more and helped spawn a cholera epidemic. The Saudi-led coalition has been criticised for its air strikes killing civilians.
Yemen's United Nations humanitarian coordinator Lise Grande said a "worst case" in an assault on Hodedia would mean 250,000 people "losing everything - even their lives".
Saudi-led coalition launches assault on Yemen’s Houthi-held key port city of Hodeida
Both the United Nations and International Committee of the Red Cross has called on all sides in Yemen's war to protect civilians following the latest air and ground assault.
United Nations chief Antonio Guterres had said that Mr Griffiths was in "intense negotiations" in an attempt to avoid a military confrontation.
"Under global humanitarian law, parties to the conflict have to do everything possible to protect civilians and ensure they have access to the assistance they need to survive", Lise Grande, UN humanitarian coordinator for Yemen, told Reuters by e-mail.
The Trump Administration, which provides military support to the coalition, had asked the Emirates to hold off on beginning an operation until after United Nations envoy Martin Griffiths presented a new plan for jump-starting peace talks.
ICRC spokeswoman Marie-Claire Feghali said the assault was "likely to exacerbate an already catastrophic humanitarian situation in Yemen", where water and electricity networks are vital to the civilian population's survival.
The Houthis, with roots in a Zaidi Shi'ite minority that ruled a thousand-year kingdom in Yemen until 1962, deny they are pawns of Iran.
Speaking to reporters this week, Mattis said that US support would continue at its current levels, and suggested USA aerial refueling, which lengthens flight times, increased the accuracy of Saudi and UAE bombing raids and so cut down on civilian casualties.
The coalition says one of the main justifications for its intervention is to protect Red Sea shipping, which brings Middle East oil and Asian goods to Europe through the Suez Canal. Saudi Arabia says Iran is backing the Houthis with weapons and logistical support - a charge Iran denies.