A Saudi-led alliance has lifted a blockade of two key airports in Yemen, broadcaster Al Arabiya reported, amid warnings that millions in the war-torn country could starve without deliveries of food aid.

The bloc closed all of Yemen's main air and sea ports on Monday, a move it said was aimed at stopping the flow of arms to Iran-backed Houthi rebels.

The blockade came in response to a ballistic missile fired at the Saudi capital Riyadh by the Houthis two days earlier.

"The coalition re-opened Aden and Seiyoun airports," said Murad al-Halimi, the transport minister of the Saudi-backed Yemeni government, according to Saudi broadcaster Al Arabiya.

He added that scheduled flights by national carrier Yemeni Airways would resume on Sunday.

The coalition continues to block traffic at the main airport in the rebel-held capital Sana'a.

The United Nations and several humanitarian groups this week warned that millions could die in Yemen from famine if the blockade, which includes relief aid, was not lifted.

Yemen, one of the Arab world's poorest countries, has been locked in a devastating power struggle between the government and the rebels in late 2014.

The conflict has created a humanitarian catastrophe in the country.

Aid groups say 17 million people of Yemen's 27 million population suffer from food insecurity.

In March 2015, Saudi Arabia and Sunni allies started an air campaign against the Houthis after they began advancing on the southern city of Aden, the temporary capital of the internationally recognised government.

Saudi Arabia fears that the rebels will give its Shi'Ite rival Iran a foothold in the Arabian Peninsula.