The Houthis, who since last week have swept through Yemeni towns along the Red Sea coast and seized islands in the Bab el-Mandeb strait at its mouth, released battlefield video overnight of fighters seizing armoured vehicles from Saudi-backed forces.
Warplanes flew overhead and huge explosions billowed into the sky from desert dunes, the video showed.
Houthi military spokesman Yahya Saree said the group had launched fresh drone and missile strikes on the major Saudi Red Sea oil port of Yanbu, and at a southern Saudi airbase at Khamis Mushait. He did not say when the strikes had taken place.
Both cities were among a wide range of locations where Saudi Arabia announced alerts on Tuesday, although there were no similar announcements on Wednesday.
Earlier, Saree said the Houthis had also shot down a Saudi F-15 fighter jet. No immediate evidence was presented of that incident.
Saree said the Saudis had carried out as many as 450 air strikes on Yemen this week. Officials in the Saudi-backed government that controls southern Yemen have acknowledged that their forces and those of Saudi Arabia were conducting air strikes on Houthi positions, though Riyadh itself has not confirmed them.
The Houthis have fired repeatedly into Saudi Arabia over the past week causing alarms over cities in the south and west. An attack blamed on Iran-aligned fighters in Iraq last week also knocked out Saudi Arabia's East-West Pipeline, the main route used to divert oil exports from the blockaded Strait of Hormuz.
Riyadh said its air defences had shot down a Houthi drone south of Mecca on Tuesday before it entered prohibited airspace over the holy city, an attack it said crossed a "red line" of threatening shrines sacred to all Muslims. Houthi spokesperson Saree denied the group had targeted Mecca, and said the Saudi reports were a set-up for propaganda purposes.
Sources told Reuters that US officials had held a meeting with the Houthis over the weekend in Oman, at which the group said it had no intention of attacking American vessels and was committed to a ceasefire reached with the US in 2025.
The extension of the war into Yemen threatens to worsen the global energy supply shortage caused by the six-month-old US-Israeli war on Iran, which has disrupted shipping through the Strait of Hormuz.
Traders say a prolonged closure of Saudi Arabia's East-West Pipeline could cut off as much as four per cent of global oil supply. Saudi Arabia has not said when operations might resume, but US Energy Secretary Chris Wright told CNBC on Tuesday that crude oil should be flowing through the pipeline within days.
Saudi Arabia has led a coalition battling the Houthis since 2015. The conflict had largely quietened under a ceasefire in recent years, but reignited when the Houthis declared a naval blockade against Saudi Arabia in July and fired at southern areas in the kingdom.
Violence has intensified sharply this month when the militant group pushed back forces aligned with the Saudi-backed internationally recognised Yemeni government.
Saudi Arabia's Crown Prince Mohammed bin Salman phoned US President Donald Trump last week seeking military support, which so far has been limited to intelligence aid.
The United States bombed the Houthis for two months in 2025, but halted that campaign after reaching what President Donald Trump described as a ceasefire that would halt attacks on ships.
Trump now faces a dilemma of whether to stand by and risk the Houthi advance worsening the global energy crisis, or provide more direct military support to the Saudis and risk extending the costly US intervention to another theatre.
