Yemen's Iran-backed Houthis targeted Saudi Arabia on Monday, hours after the rebels accused the kingdom of attacking Sanaa airport, in what is seen as the biggest escalation between the two sides in years, that threatens to upend a frozen conflict amid a volatile situation in the Middle East.

The Saudi-backed Yemeni government claimed responsibility for the attack on the Houthi-held airport, saying it wanted to prevent an Iranian plane from landing.

It came after they failed to convince a Houthi delegation that went to Tehran for the late Iranian supreme leader Ali Khamenei's funeral to board a flight on domestic carrier Yemenia instead.

"Air defenses dealt with a ballistic missile threat launched by Houthi militia towards the southern region," coalition spokesperson Turki al-Maliki said in a social media post.

Earlier, Houthi military spokesperson Yahya Saree accused Saudi Arabia of "ending the de-escalation phase" and warned that "this aggression will not go unanswered or unpunished."