Forces of the Saudi-led coalition fighting in Yemen have recaptured several key areas around Bab el-Mandeb Strait from Iran-backed Houthi rebels, Yemeni officials said Monday.

The officials said forces allied with the internationally recognized government have retaken the crucial town of Dhubab just north of the strait. They also captured the towns of Bab and Hadeid, said the officials, who spoke on condition of anonymity because they were not authorized to speak to reporters. Witnesses said they saw government tanks and forces entering the towns.

The government push came as part of a major offensive launched early Monday under an air cover by a Saudi military coalition, aiming to retake all territory held by the Houthis.

However, the offensive came just after the rebels said they had captured more territory in the south-western part of Yemen, taking the key town of Turbah in a blow to the Saudi-backed forces as they advanced toward the strategic provincial capital of Taiz, Yemen’s third-largest city.

The Saudi-led coalition spokesperson, Maj Gen Turki al-Malki, said 100 fighter jets were providing support to the forces of Yemen’s internationally recognized government fighting against the Houthis. He said the coalition has secured “air protection” of the strategic Bab el-Mandeb Strait and destroyed hundreds of Houthi targets as part of the ongoing campaign.

Marco Rubio told reporters that it was expected that the Saudi-backed government in Yemen would hit back at the rebels to reclaim territory. Asked if the Saudi-led coalition coordinated the action with the United States, the US secretary of state said that Saudi Arabia and the US have a defense agreement but wouldn’t offer more details.

He said the Yemeni government was ousted from some of its territory by a Houthi campaign and the Saudis have come under attack, and “they have a right to defend themselves”.

The new push sets an ambitious goal for the embattled government, which recently lost swathes of the country’s Red Sea coastline and areas around the Bab al-Mandab strait – a chokepoint for international shipping – after a lightning offensive by the Iran-backed Houthis.

Yemen’s internationally recognised government has struggled to roll back the surge, even with the military support of Saudi Arabia. The Houthis have increasingly targeted Saudi Arabia in recent weeks, and on Sunday said they had attacked oil infrastructure in the capital again.

The statement came just hours after the Houthis cut a vital supply route linking the besieged city of Taiz with the government’s interim capital, Aden, according to four security sources.

The Houthi advance followed days of heavy fighting in and around the city.

“We were informed that the Houthis had taken control of the al-Safiya area, where they cut the main road and took control of the police station,” a police source in the area said.

Three sources with the Yemeni military also confirmed Houthi control over the area and the supply route, with traffic along the road halted and the group now surrounding Taiz city. Fighting in the area was ongoing, they added.

Sources from both sides told AFP on Sunday that fighting in and around the western province of Taiz had killed more than 70 people over the past day.

Sources from the internationally recognised government reported that 34 government troops were killed – 20 on the edge of Taiz province in neighbouring Lahj – while Houthi military sources said 39 of their fighters were killed in fighting across Taiz and in border areas with Lahj.

Taiz city itself remains under the control of government forces but has long been besieged from the north, east and west by Houthi fighters and remains one of the main fronts in Yemen’s long-running civil war.

A Houthi military spokesperson, Yahya Saree, said on Sunday the group launched ballistic missiles and drones at Saudi energy company Aramco’s sites in Riyadh and in Khurais area in the east, causing large fires.

The attacks were in response to what the Houthis claimed were 50 Saudi-led ‌air and missile strikes in Yemen in the past 12 hours.

There was no immediate confirmation from Saudi Arabia.

Saudi oil exports were already under pressure due to Iran’s blockade of the strait of Hormuz in the Gulf.

The Houthi’s Al-Masirah TV channel reported Saudi strikes on Sunday in the northern governorates of al-Jawf and Saada, saying at least two people had been wounded.

With Reuters and Agence France-Presse