A Saudi-led coalition has warned Yemen's rebels threaten ships in the Red Sea through their control of a key port, days after rebel warnings over a coalition blockade.

"The port of Hodeida is a launching pad for terrorist operations threatening navigation in the Red Sea and the Bab al-Mandab Strait," coalition spokesman Turki al-Maliki said late Wednesday.

The Red Sea is a key shipping route for world trade that connects the Middle East to Europe via the Suez Canal. The Bab al-Mandab Strait is the southern entrance to the Red Sea.

The Shiite Huthi rebels control the main port of Hodeida among a string of Red Sea ports on Yemen's western coast that are vital entry points for food imports and aid.

Maliki spoke after the rebels on Monday threatened to cut off Red Sea traffic unless Saudi Arabia and its allies lifted a blockade on Yemen's ports and main international airport.

In November, the coalition tightened the blockade after the Huthis fired a missile into Saudi Arabia that was intercepted near Riyadh's international airport.

The blockade has massively reduced the amount of food and relief reaching the country, international aid groups say, even though the coalition has since allowed certain aid deliveries in.

More than 9,000 people have been killed since the Saudi-led coalition joined the Yemeni government in its fight against the Huthis in March 2015.

The coalition, which has warships positioned in the Red Sea, accuses Iran of backing the Huthis.

Yemen was highly dependent on food imports even before 2015, and the United Nations has warned the country now stands on the brink of famine.