Burnt out cars were seen on the streets of the city, whose port serves as a key lifeline to the impoverished country.
The U.S. and United Kingdom, major arms suppliers to the Saudi coalition, have recently called for a cease-fire in Yemen and the launch of U.N. -led political talks to end the Saudi-Iran proxy war.
The move comes ahead of another proposed round of peace talks in Sweden later this month, it said.
After almost four years of conflict between Yemen's Iran-linked Huthis and a pro-government military alliance led by Saudi Arabia and the UAE, the fight this month reached rebel-held Hodeida, home to Yemen's lifeline port.
The conflict has killed more than 10,000 people and has left 14 million people on the brink of starvation, the United Nations says.
The port's deputy director, Yahya Sharafeddine, said the main entrance to the docks had been "the target of air raids" but was fully functioning Tuesday. He reported three wounded guards.
UN Secretary General Antonio Guterres warned on Monday of a possible "catastrophic situation" if the port is destroyed.
Four employees in Hodeida port who requested anonymity told AFP that a rebel commander had been killed in the Monday attack.
"Fighting is fierce. There have been gains on the coalition side over the a year ago as they've moved up the coast towards Hodeida, but the Huthis are fighting back", said Kristine Beckerle, Yemen researcher at Human Rights Watch.
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Pentagon chief Jim Mattis on Saturday confirmed his country had halted its controversial aerial refuelling support for coalition aircraft involved in the Yemen war.
During the past few days, the government forces made significant progress despite a large number of landmines and booby-trapped buildings, in addition to professional Houthi snipers who took positions on buildings inside residential neighborhoods, local military sources said.
Yemeni government forces covered by the coalition's air and naval forces continue to engage in heavy fighting with the rebels, known as Houthis.
"We are not hearing explosions like we have for the past two weeks". Who is winning, and what's next for the crucial port city?
Aid groups have urged both parties in the conflict to keep roads open to allow civilians to escape and the transportation of aid through the Hodeida port.
The ongoing fighting left almost 600 people killed in Hodeidah from both warring parties during weeks of ferocious fighting and intensified airstrikes launched by the Saudi Arabia-led coalition.
Almost four years into the war, there has been an increase in global pressure to end the fighting in Hodeida, whose docks are the entry point for some 80 percent of food imports and humanitarian aid into impoverished Yemen.
The Hodeidah offensive has sparked global outcry unprecedented in almost four years of conflict between Houthis, who are linked to Iran, and the Saudi-backed government.