Early on Wednesday, convoys of vehicles headed toward the rebel-held city as heavy gunfire rang out.
The Arab states have been fighting since 2015 to unseat them, restore an exiled Saudi-backed government and halt what they see as Iranian expansionism.
Aid agencies warned that the crucial battle in the three-year-old conflict could push the Arab world's poorest country into further chaos.
Through this period and in many occasions, the Arab coalition has called for an global action to put a halt to rockets and weapons smuggling through aid campaigns entering Yemen from Hodeidah port, demanding to no vain, that the worldwide community should send humanitarian organizations to monitor the aid shipment entering Yemen.
"Hodeidah is absolutely essential to the preserving of life", the United Nation's emergency relief coordinator, Mark Lowcock, said this week.
The International Committee of the Red Cross said any battle for Hodeidah would exacerbate the suffering of the population.
Its leader, exiled President Abd-Rabbu Mansour al-Hadi, said his government had proposed compromises but would not let the Houthis hold the Yemeni people "hostage to a prolonged war which the Houthis ignited".
The request for the Security Council meeting came after the United Nations envoy for Yemen, Martin Griffiths, said he was still holding negotiations on keeping the key port open to aid deliveries. Lasting peace and stability in Yemen will require dialogue and negotiation.
Saudi-led coalition warplanes and Apache helicopters provided "continuous" air support to pro-government forces, striking Huthi positions, military sources said.
Last month, the committee advanced legislation making U.S. midair refueling contingent on Saudi and Emirati efforts to engage in diplomacy, ensure access of humanitarian goods, reduce civilian casualties and avoid damaging critical infrastructure.
The Foreign Secretary Boris Johnson called on all sides to prioritise the protection of civilians and respect humanitarian law.
The coalition says victory could break the stalemate in the war and force the Houthis to the negotiating table.
The new United Nations envoy to Yemen, Martin Griffiths, tweeted that he was "extremely concerned" by the violence, calling on all parties to exercise restraint.
Secretary of State Mike Pompeo stated on Monday that the United States is "closely following developments in Hudaydah", and added the USA wants to preserve "the free flow of humanitarian aid and life-saving commercial imports".
A statement was issued in the name of Hadi's regime declaring, "The liberation of Hodeidah port is the start of the fall of the Houthi militia and will secure marine shipping in Bab al-Mandeb strait and cut off the hands of Iran, which has long-drowned Yemen in weapons that shed precious Yemen blood".
Yemen lies beside the southern mouth of the Red Sea, one of the world's most important trade routes, where oil tankers pass from the Middle East through the Suez Canal to Europe. They have always been restricting imports into Hodeidah to prevent what they say is Iranian traffic of missiles to the Houthis, and say they can swiftly improve food supplies once they control the port. The accusations are denied by the group and Iran.
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