The United Nations and other aid groups already had pulled their worldwide staff from Hodeidah before the rumoured assault.
"We fear that a prolonged attack or siege on Hodeidah could be catastrophic for civilians", Lise Grande, the UN's head Yemen humanitarian coordinator, previously told the Wall Street Journal, adding that 250,000 of the city's 400,000 people could be killed.
Saudi Arabia and its allies seek to attack the Yemeni city of Hudaydah.
Yemen's biggest port, Hodeidah is the lifeline for the majority of Yemen's population, which lives in Houthi territory.
Yemen's exiled government "has exhausted all peaceful and political means to remove the Houthi militia from the port of Hudaida", it said in a statement.
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 Saudi-led coalition did not immediately acknowledge the incident.
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.
Forces loyal to Yemen's exiled government and irregular fighters led by Emirati troops had neared Hudaida in recent days.
The civil war in Yemen has killed about 10,000 people over the past three years and created what the United Nations says is the world's worst humanitarian disaster.
The sources said Yemeni forces allied to the Saudi-led coalition - drawn from southern separatists, local units from the Red Sea coastal plain and a battalion led by a nephew of late former president Ali Abdullah Saleh - had advanced and were "at the doors" of Hodeidah airport. This has made it by far the most important port for humanitarian aid, with estimates that as much as 70% of aid comes through the port.
Defense Secretary Jim Mattis on Monday acknowledged the USA continues to provide support to the Saudi-led coalition. It said: "The Emiratis have informed us today that they will now give a three-day grace period for the United Nations (and their partners) to leave the city".
The war pits the Houthis against the Western-backed Sunni Muslim states, which intervened in 2015 to restore the exiled government and thwart what Riyadh and Abu Dhabi see as expansionist aims of their Shi'ite Muslim foe Iran.
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.
The UAE has said coalition forces plan to keep the port operational but warned the Houthis could sabotage infrastructure and place land and sea mines as they withdrew.
He said the coalition wanted the United Nations to take control of the port but it was prepared to take military action if the Houthis refused to withdraw. Meanwhile, the UN and western nations say Iran has supplied the Houthis with weapons from assault rifles up to the ballistic missiles they have fired deep into Saudi Arabia, including at the capital, Riyadh. The accusations are denied by the group and Iran.
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