Yemen's Saudi-backed government has announced a new military operation to retake all territory held by the Houthis, a bold declaration made slightly awkward by the fact that the Houthis were, at that very moment, busy taking more territory.

Rashad al-Alimi, head of Yemen's presidential council, delivered the announcement on Sunday: "I announce today the start of military operations to retake the remaining territories of the republic and extend the authority of the state and its institutions across the entire national territory." It is an ambitious goal for a government that recently lost swathes of the country's Red Sea coastline and areas around the Bab al-Mandab strait - a chokepoint for international shipping - following a lightning offensive by the Iran-backed Houthis.

Yemen's internationally recognised government has struggled to roll back the surge even with military support from Saudi Arabia, which itself has been increasingly targeted by the Houthis in recent weeks. On Sunday, the group said it had attacked oil infrastructure in the Saudi capital again.

The presidential statement landed 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 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 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. Government sources reported 34 government troops 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 government control 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.

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 the Khurais area in the east, causing large fires. The attacks were framed as a 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 Houthis' 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.