Iran-backed Shiite Huthi rebels have launched a string of ballistic missile attacks on Saudi Arabia, which shares a border with the war-torn country, from the northern province.

In the latest attack, the coalition said it shot down a missile late Wednesday fired by the Huthis who said they targeted storage tanks of Saudi oil giant Aramco in the border province of Jizan.

Hundreds of soldiers from Saudi Arabia and Sudan, both allied with the government in its war against the rebels, have arrived in the north to reinforce Yemen's troops deployed around Saada, Yemeni military officials said.

Prime Minister Ahmed Ben Dagher hailed the operation as "the end of Iran's confessional plans for Yemen, executed by its Huthi allies".

The rebels say their missile attacks on Saudi Arabia are retaliation for air raids by the Riyadh-led military coalition.

Both the coalition and the United States -- a key ally of Saudi Arabia -- have accused Iran of arming the Huthi rebels.

Tehran denies sending military supplies to the insurgents but has openly said it supports the Huthis' fight in Yemen.

According to sources in the Yemeni army, the government alliance has advanced "several kilometres" towards the town of Saada, capital of the province of the same name, since the reinforcements arrived.

The embattled government of President Abedrabbo Mansour Hadi was driven out of Yemen's capital in 2014 by the Huthis, who control Sanaa and much of northern Yemen.

The coalition led by mainly Sunni Saudi Arabia has since struggled to close in on rebel strongholds, including Maarib -- a key province in central Yemen -- and Hodeida, the country's largest port.

Nearly 10,000 people have been killed since the coalition joined the Yemen war in 2015, triggering what the United Nations has called the world's largest humanitarian crisis.

Rights groups have warned that both the coalition and rebels are potentially guilty of war crimes. The UN last year blacklisted the coalition for the maiming and killing of children.