"The battle of the Yemeni people to liberate Hodeida is inevitable, whether through peace or war", the statement said.
At least 150 people have been killed in 24 hours of clashes in the Yemeni port city of Hodeida, medics said on Monday, as Britain's top diplomat visited Riyadh seeking to boost global calls for a ceasefire.
But four other port employees told AFP on condition of anonymity that a rebel commander, along with three of his guards, had been killed in Monday's bombing.
British Foreign Secretary Jeremy Hunt met with Saudi King Salman on Monday during a visit to the kingdom to press its rulers to support United Nations efforts to end the conflict.
Western governments that support the coalition with arms and intelligence have toughened their stance on Yemen after the murder of journalist Jamal Kashoggi at the Saudi consulate in Istanbul on October 2 sparked a global outcry and opened Riyadh to possible sanctions.
At least eight "passengers" fleeing escalating fighting in Yemen's war-torn port city of Hodeidah were killed on Tuesday when a Saudi-led coalition airstrike hit a bus, Houthi rebel-controlled Saba news agency reported.
Hodeidah is an entry point for 80 percent of the impoverished country's food imports and relief supplies.
UN Secretary-General Antonio Guterres has warned that the destruction of the Yemeni port of Hodeidah, a vital lifeline for millions of starving civilians, could trigger a "catastrophic" situation.
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.
Pro-government troops reached residential neighbourhoods in Hodeida Sunday, triggering fears for civilians who could be trapped in the city. "During the night we heard sporadic gunfire but then situation seems stable todat", one Hodeida resident told AFP by telephone.
The coalition abandoned a previous offensive on Hodeidah last June without any gains amid global concern over a humanitarian catastrophe to give peace talks a chance.
After the Houthis failed to show up for talks in Geneva in September, Griffiths got both sides to agree to confidence-building measures to set the table for a new dialogue, including United Nations administration of Hodeidah, prisoner exchanges and the reopening of airports in Sanaa and Aden to facilitate the delivery of aid.
The alliance accuses Iran of smuggling arms to the Houthis through the Hodeida port.