Monday's strikes, in which port staff said four rebels were killed and four wounded, was the first to hit the docks in 12 days of intensified bombardment and ground fighting in the Red Sea coastal city of some 600,000 people, many of whom have fled or now fear a siege.
Other residents have said they feared being trapped in the city, where only one major exit route is still open to traffic and the transport of food and aid, on the northern edge of the city.
The vital docks, through which 80 percent of Yemen's commercial imports and almost all United Nations supervised humanitarian aid pass, has been at the centre of worldwide concern about a new drive to recapture Hodeida which the Yemeni government launched with Saudi-led support on November 1.
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.
Yemeni pro-government forces gather at a checkpoint in a street on the eastern outskirts of Hodeida as they continue to battle for the control of the city from Huthi rebels.
The multi-pronged assault, backed by the Saudi Arabia-led coalition, has overwhelmed many Houthi-controlled neighborhoods of Hodeidah, sparking nonstop street-to-street fights between the advancing government troops and the Houthi rebels holed up in the city.
Asked about the possibility of a ceasefire, a coalition spokesman told reporters in Riyadh that "the operation is still ongoing", adding that it was meant to pressure the rebels to come to the negotiating table.
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Kick-starting peace talks is now a key goal for Western powers, who turned their focus to Yemen after the high-profile murder of Saudi Arabian journalist Jamal Khashoggi, a vocal critic of Saudi Arabia's Crown Prince Mohammed bin Salman.
The deal comes just one day after UK Foreign Secretary Jeremy Hunt called on Saudi Arabia to end the Yemen conflict, suggesting that global pressure could help lead to a settlement. He reported three wounded guards.
"If the port at Hodeida is destroyed, that could create an absolutely catastrophic situation", UN Secretary General Antonio Guterres warned.
The alliance accuses Iran of smuggling arms to the Houthis through the Hodeida port.
"The coalition sees military pressure as key to ensuring the Huthis come to the table and are ready to compromise", said Dickinson.
"Serious consideration is being given to a set of political ideas and confidence-building measures that would allow for the start of political talks in Sweden by the end of November", the statement continued.