The raids on the country's main air gateway came just hours after UN workers were evacuated following deadly fighting that has sent tensions between Tehran and other Middle East powers soaring. India and Pakistan also moved to airlift their citizens from the chaos-wracked country.
India said it had received permission from the Arab coalition to airlift its stranded citizens and would also send a ship.
Yemen's President Abedrabbo Mansour Hadi has urged his Arab allies to keep up the bombing until the Huthi Shiite rebels are defeated, branding them Iran's "puppet".
Arab League chief Nabil al-Arabi said at a regional summit in Egypt today the offensive would go on until the rebels "surrender" their weapons and withdraw from areas they seized.
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The Huthis and allied renegade military units have overrun much of the country and prompted Hadi to flee what had been his last remaining refuge in the main southern city Aden for Saudi Arabia.
Dozens of people have been killed in clashes in Aden in recent days, dimming prospects of Hadi returning any time soon.
In the capital, witnesses reported hearing three loud explosions and seeing a large fire when Sanaa International Airport was bombed during a fourth night of Saudi-led air raids.
"This was the first time they hit the runway" since the campaign began, an aviation source said. "The airport is completely out of service."
A civil aviation official at the airport later told AFP that work to repair the runway had begun.
More than 200 staff from the UN, foreign embassies and other organisations had been flown out from the airport yesterday.
Overnight air strikes hit the headquarters of the rebel republican guard at Al-Subaha base in Sanaa, killing 15 soldiers, a military official said.
The Huthis are backed by army units loyal to former president Ali Abdullah Saleh, who stepped down in 2012 after a year-long popular uprising and is accused of supporting the rebels.