The Houthis said Saudi Arabia retaliated with strikes on Tuesday after the group targeted oil facilities, wounding dozens, as deadly fighting reignited in Yemen after a Houthi offensive towards the Red Sea's Bab al-Mandab chokepoint.

The rapid round of strikes and counter-strikes follows the unravelling of a four-year truce between the Houthis and the Saudi-backed government in July.

Analysts dispute the extent to which the Houthis are acting independently or following the wishes of their Iranian backers, but on Tuesday US Secretary of State Marco Rubio insisted that "behind some of this is clearly the Iranian hand".

On Thursday, the Houthis launched a campaign to seize territory near the Bab al-Mandab strait, an increasingly important route for Saudi oil after Iran blockaded the Strait of Hormuz, choking Gulf exports.

The fighting has left more than 500 people dead, mostly combatants from both sides, according to an AFP tally based on sources from each camp.