Three commercial ships carrying diesel arrived in Yemen's Houthi-held port city of Hodeidah on Thursday, after they were permitted by the Saudi-led coalition following a 49-day wait on the Red Sea.

About 20,000 metric tonnes of diesel will be delivered as soon as possible throughout the country to meet the urgent needs in hospitals and other vital facilities, the Houthi-controlled Yemen Petroleum Company said in a statement.

"The amount is very few and would cover local needs for a few days only," it said, urging the coalition naval forces to allow the entry of other 10 commercial ships carrying more than 106,000 metric tonnes of petrol and 159,000 metric tonnes of diesel, which they have been waiting for permits for nearly two months to enter Hodeidah port.

There was no immediate comment from the coalition on the Yemeni rebels' claim.

Yemen has been experiencing prolonged severe fuel crisis because of economic blockade imposed by the coalition.

The blockade has caused the world's worst humanitarian crisis. Nearly 80 percent of the total population, 24.1 million people, need some form of humanitarian assistance and protection.

A total of 10 million people are a step away from famine and starvation and 7 million are malnourished, according to the UN Humanitarian Coordinator in Yemen.

Saudi Arabia has been leading an Arab military coalition against Iran-allied Houthis in Yemen for more than four years in support of exiled government of Yemeni President Abd-Rabbu Mansour Hadi.