Houthi officials said on Monday that the Iran-aligned rebels had taken over the two islands just as Saudi-backed government forces tried to claw back territory from the rebels' swift advances around the Bab el-Mandeb Strait, a crucial shipping alternative to the Strait of Hormuz.
Iran largely closed the Strait of Hormuz - through which a fifth of the world's traded oil and gas transits in peacetime - in the opening days of the war with the US and Israel.
Saudi vessels have since used the Bab el-Mandeb Strait, which leads out of the Red Sea, for crude oil exports.
The Houthis' latest takeover, following the seizure of the Red Sea port of Mocha and a strategic island last week, puts more pressure on Saudi shipments and in turn global oil supplies and prices.
Nearly 94,000 people have fled their homes in Yemen since fighting between Houthi rebels and government forces escalated this month, the International Organisation for Migration said on Monday.
The worst-hit areas are Taiz and Lahj, where 48,000 have been displaced, the United Nations agency said, adding that more than 2000 people have fled across the sea into Djibouti.
About 200 schools have been converted to shelters in southwestern Yemen to absorb an influx of families, aid group International Rescue Committee said.
Fears are mounting that Yemen is inching closer to a return to a civil war that killed 150,000 before a 2022 ceasefire.
The World Health Organisation said more than 500 people were killed in a week-long period ending on Saturday, a sharp increase.
