Hodeida remained open and processing ships despite the offensive, port authorities said.

The Iran-backed Huthi rebels who control the Red Sea port city -- home to 600,000 people -- reported "two enemy air strikes on the (Hodeida) area" via their news outlet Al-Masirah.

The coalition could not immediately be reached for comment, but the previous day coalition sources told AFP that 18 air strikes had been carried out on Huthi positions around Hodeida.

Yemeni government forces and their Saudi and Emirati allies began an offensive aimed at retaking Hodeida from the Huthis on Wednesday, pressing toward the airport south of the city.

The UAE, a driving force in the coalition, said four of its troops were killed on the first day of the offensive. It did not state when or where the soldiers were killed, but said at least one was a navy officer.

On Wednesday, the Huthi rebels said they had targeted a coalition ship off the coast of Hodeida with two missiles, with their outlet Al-Masirah claiming a direct hit.

On shore, the offensive has reached the outskirts of Hodeida airport which is in rebel hands.

"The forces managed to liberate new strategic areas in Al Duraihimi district and areas adjacent to Hodeida airport after penetrating the Huthi militia's frontlines," the state-run Saudi Press Agency reported Thursday.

The offensive is controversial because the port serves as the entry point for 70 percent of Yemen's imports, as the country teeters on the brink of famine.

On Thursday, authorities at the port said it remained open to ships.

"We still have seven ships in the port. The work in the port is normal. And we have five other ships standing by waiting outside to enter," port director Dawood Fadel told AFP.

Two Saudi and UAE aid ships were in the waters off Hodeida, coalition spokesman Turki al-Maliki told Saudi state media.

Saudi Arabia, which intervened against the Iran-backed Huthis in 2015 with the goal of restoring Yemen's government to power, has pledged to ensure a continuous flow of aid to its neighbour.