The Houthis now control the country's entire Red Sea coastline after capturing the key port city of Mocha in Taiz province from government forces earlier this week.
Mocha is located about 90km west of the city of Taiz.
Government forces currently still control parts of Taiz province including its capital city of the same name but fighting in the area continues.
Military sources said that government forces had again attacked Houthi positions in the Taiz area.
Houthi-owned television channel al-Masirah reported that Saudi Arabia had bombed targets to support Yemeni pro-government forces.
According to Houthi-controlled news agency Saba, the Iran-aligned rebels fired at weapons depots and command centres in Saudi Arabia.
The Houthis have been fighting Yemen's Saudi-backed government for more than a decade.
A 2022 truce left the conflict largely frozen but also with little prospect of an end to the war.
Fighting has flared up again amid the wider war involving Iran, plunging already impoverished Yemen - which borders Saudi Arabia and Oman -deeper into civil war.
The United Nations International Organisation for Migration reports that the number of internally displaced people has risen rapidly in recent days to nearly 86,000.
More than 82,000 people have fled fighting since the beginning of September, with more than 2000 people crossing the Red Sea strait and fleeing to Djibouti.
Earlier UN estimates from 2021 said that more than 150,000 people had been killed in the fighting while another 220,000 had died as a result of indirect consequences of the war including hunger and disease.
About 22 million people in Yemen depend on humanitarian assistance.
The Houthis' recent advance along the country's western coast will allow the rebels to ramp up attacks and blockades on shipping launched amid resurging tensions with Saudi Arabia.
A Houthi spokesman said that shipping would remain safe, with the exception of Saudi vessels.
