Saudi Arabia has bombed the northern stronghold of Yemen's Shiite rebels and other key military installations as a coalition led by the Gulf kingdom carried out air strikes for a second day.

The military action is turning impoverished and chaotic Yemen into a new front in the rivalry between Sunni heavyweight Saudi Arabia and Shiite power Iran, which supports the rebels known as Houthis.

Heavy air strikes targeted Saada, the stronghold of the Houthis, focusing on locations where rebel leader Abdul-Malik al-Houthi might be.

Saudi warplanes also bombed the al-Sana army camp in the Arhab region north-east of the capital Sanaa, run by commanders loyal to former president Ali Abdullah Saleh.

The military official said other strikes targeted army camps outside Sanaa in al-Dhale and Lahj provinces, including al-Annad base, where about 100 US military advisers had been based but were forced to withdraw last weekend due to deteriorating security conditions.

In the capital itself, heavy air strikes came in waves throughout the night.

Explosions rocked the city and anti-aircraft guns were heard returning fire. At least 18 civilians, including six children, were killed and the casualty count was expected to rise.