It said troops, backed by the Saudi-led coalition are now about eight kilometers (five miles) from the rebel-held Hodeida.
Hodeida is a lifeline for the majority of Yemen's population and aid agencies earlier this week had warned of a humanitarian catastrophe if the attack went ahead. About 8.4 million people are at risk of starvation.
The United Arab Emirates' state-run news agency published the names and ranks of the four soldiers, but did not give further details on how they died. We are concerned about missiles and shells.
On Thursday, the International Committee of the Red Cross said it had pulled 71 staff members out of Yemen after a series of security incidents and threats. In a report in January, the panel cited the fact that ships coming into the port face random inspections, require United Nations approval and that no weapons have been seized since March 2017.
The United Nations said it was engaged in "intense" shuttle diplomacy between the Houthis and coalition leaders Saudi Arabia and the UAE to avert the attack.
The officials said government forces have headed to the eastern coast aiming at cutting off a rebel supply line between Hodeida and Sanaa.
The U.S. has not publicly opposed the assault but has urged the coalition to ensure that humanitarian aid deliveries to the port continue. The Red Sea port is the main entry for food into a country on the brink of starvation.
Gunfire has erupted near Yemen's port city of Hodeida as a Saudi-led coalition's deadline expired for Shiite rebels there to withdraw.
Abdallah Al-Mouallimi said the ships - from Saudi Arabia and the United Arab Emirates - are part of coalition efforts "toward ensuring abundant humanitarian supplies" to Hodeida during the offensive.
Saudi-owned satellite news channels later announced the battle had begun, citing military sources. He said the rebels had countered "hostile naval warships" off the coasty of al-Olifika, to the south. "Everything depends on that port", she said.
The coalition's initial battle plan appears to involve a pincer movement.
Forces loyal to Yemen's exiled government and irregular fighters led by Emirati troops had neared Hodeida in recent days.
The officials spoke on condition in anonymity because they weren't authorized to brief reporters.
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 Iran.
The United Nations and other aid groups already had pulled their worldwide staff from Hodeida ahead of the assault. He said the U.N. Security Council must act to secure a cease-fire before the people of Hodeida "suffer the same fate as those in Aleppo, Mosul or Raqqa".
It would be the first time since they joined the war on behalf of Yemen's exiled government that the foreign armies have attempted to capture such a well-defended major city. Saudi-led airstrikes have killed large numbers of civilians and damaged vital infrastructure.
Troops in a Saudi-led coalition have captured a town south of the Yemen port city of Hodeida as fierce fighting and air strikes pounded the area, officials said.