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Mahra province in the far east of Yemen and the neighbouring Dhofar region of Oman are the only parts of the Arabian Peninsula that have a monsoon climate governed by the tropical weather systems of the Indian Ocean.

Mountains rising to 1,300 metres (4,300 feet) separate a fertile coastal strip from the infamous Empty Quarter in the vast desert interior.

Most of Luban's casualties were reported in coastal districts of Mahra, where two people were killed and 33 injured by widespread flooding, the UN Office for the Coordination of Humanitarian Affairs (UNOCHA) said.

In Oman, the civil defence said one man was found dead in Dhofar.

Mahra governor Rajeh Bakrit said on Monday the province had been devastated by the storm.

"The situation is catastrophic in the province and beyond the capabilities of the local authorities," he said, according to the government-run Saba news agency.

Yemen President Abedrabbo Mansour Hadi cited the "failure" of the government's efforts to respond to the "catastrophic" storm as one of the reasons for dismissing prime minister Ahmed bin Dagher late on Monday.

UNOCHA said more than 2,000 families had been significantly affected by the flooding in Mahra with many finding emergency shelter in public buildings.

It warned there were expected to be more casualties and homes washed away in areas that had yet to be reached by emergency teams.

In May, Cyclone Mekunu smashed into southern Oman and the Yemeni island of Socotra, killing at least 11 people.

Residents of Mahra and Socotra have long complained of being left to fend for themselves as Hadi's beleaguered government focuses on wars against Houthi rebels, who have controlled the capital Sanaa and much of the north since 2014, and against jihadists, who have a major presence in neighbouring Hadramawt province.