Yemeni forces, supported by a Saudi-led coalition, said they advanced against Iran-allied rebels around Hodeidah on Saturday, a day after the government fighters started a major offensive to retake the vital port city.
Military sources told dpa that government forces had gained territory from the Houthi rebels on the eastern and southern outskirts of Hodeidah.
The claim could not be independently verified.
"The army forces will not stop until they take control of the strategic Hodeidah port," a military source said on condition of anonymity.
An estimated 80 per cent of imports and aid reach Yemen through Hodeidah's port in western Yemen.
Residents in Hodeidah said that the Saudi-led coalition overnight carried out a series of airstrikes against rebels on the edges of the Red Sea city. No casualties were given.
One of the Arab world's poorest countries, Yemen has been embroiled in a disastrous power struggle between the Saudi-backed government and the Houthis since late 2014, when the rebels seized the capital Sana'a and Hodeidah.
Aid agencies have repeatedly warned that the military campaign on Hodeidah would have devastating consequences for the country's residents, who are already on the brink of famine.
Last month, the UN's relief chief warned that Yemen was in danger of being engulfed by an imminent famine that could affect 14 million people, or around half the population.
The ongoing violence comes amid international pressure on Yemen's warring sides to stop the devastating conflict.