The allegations follow an intensified aerial bombing campaign by the coalition against the Houthis in retaliation for the recent deadly attacks on the kingdom.
The Saudi-led coalition has accused Iran and Hezbollah of helping Yemen's Houthi to launch missiles and drones at the kingdom, where two people were killed.
Coalition spokesperson Turki al Maliki told a news conference on Sunday that the Houthis were "militarising" Sanaa airport and using it as a "main centre for launching ballistic missiles and drones" towards the kingdom.
Malki showed reporters a video clip which he said depicted "the headquarters of Iranian and Hezbollah experts at the airport" where, he alleged, "Hezbollah is training the Houthis to booby-trap and use drones".
Maliki also showed other clips which he said depicted a Hezbollah member placing explosives in a drone, and a man he identified as a Hezbollah official telling Houthi members "we must strengthen our ranks".
The footage could not be independently verified.
Tehran denies the charges. Lebanon's Iran-backed Shia movement Hezbollah has previously denied sending fighters or weapons to Yemen.
Malki said the international community must "stop hostile acts by this terrorist organisation," a reference to Hezbollah.
Since January 2018 the Houthis have launched 430 ballistic missiles and 850 drones towards Saudi Arabia, he said.
Malki also accused Iran's ambassador to Sanaa, who died of Covid-19 last week after his evacuation from Yemen, of "leading the planning of military operations in Marib" – the Yemeni government's last stronghold in the north.
READ MORE: Saudi coalition hits Houthi camp in Yemen's Sanaa as air strikes ramp up
Sunday evening the coalition announced it had made new strikes near an air force academy in Sanaa to prevent weapons from being moved.
Earlier on the same day, the coalition said it had struck a Houthi rebel camp in Sanaa, destroying weapons warehouses.
On Saturday, the coalition launched what it called a "large-scale" military operation against the Houthis after the rebel missile strike that hit Jazan.
Its raids left three civilians dead, including a child and a woman, Yemeni medics told the AFP news agency.
Rights groups have criticised the coalition for civilian casualties in its years-long aerial bombardment.
The coalition maintains its operations are carried out in accordance with international humanitarian law, repeatedly urging the Houthis against using civilians as human shields.
The Houthis warned in a statement that they will "face escalation with escalation".
Since the coalition intervened almost seven years ago to support Yemen's government, Saudi Arabia has regularly accused Iran of supplying the Houthis with weapons and Hezbollah of training the fighters.
READ MORE: Saudi-led coalition launches major Yemen operation after deadly strike