Iran's ambassador flew out of the rebel-held Yemeni capital to receive Covid treatment Saturday in a rare exemption from an air blockade enforced by a Saudi-led coalition, Saudi and Iranian officials said.

"The ambassador left on an Iraqi aircraft and is probably now in Baghdad," a senior Saudi official familiar with Yemeni affairs told AFP.

He said the flight was organised at the request of Yemen's Huthi rebels and agreed by Saudi authorities following mediation by Iraq and Oman.

Iraq has hosted several exploratory meetings between Iranian and Saudi officials seeking a thaw in relations after years of proxy wars around the region.

Oman is the only Gulf Arab state that has remained neutral in the Yemen conflict and has frequently mediated with the rebels.

In Tehran, a foreign ministry spokesman said that the ambassador had been suffering from Covid-19 for several days and that arrangements had been made for his evacuation.

In Sanaa, rebel spokesman Mohammed Abdul Salam tweeted that an understanding between Iran and Saudi Arabia brokered by Iraq had allowed the ambassador's evacuation on health grounds.

Tehran is the only government that recognises the rebel administration in Sanaa, and in October last year it sent Hassan Eyrlou there as ambassador. It gave no details on how he had reached the city despite the blockade.

The Saudi-led coalition which has fought alongside forces loyal to Yemen's internationally recognised government since 2015 has repeatedly accused Iran of arming the rebels, a charge it has consistently denied.

The Wall Street Journal reported Friday that the Huthi request for a flight out for the ambassador was being seen by Saudi officials as a "sign of strains between Tehran and the militant group".

But speaking to AFP on Saturday, a second Saudi official confirmed that the ambassador's departure had been a medical evacuation.

"The Iranians told us through the Omanis that their ambassador had contracted Covid and must get out," the official said.

"We agreed to let him out for humanitarian reasons."

Yemen's healthcare system has been devastated by seven years of war which has triggered what the United Nations has described as the world's worst humanitarian crisis.