Rains are expected to continue for two more days, drenching the area with more than 100mm of rain, nearly six times its annual average, weather experts WASM said on Twitter.
Oman police earlier reported that the man died after floods swept him away with his auto near Salalah, Oman's second-largest city, while the girl died when a gust of wind smashed her into a wall. Yemenis, Indians and Sudanese were among those missing and officials feared some may be dead.
Salah is home to about 2,00,000 people and portion of it lost power after being hit by the storm. Those deaths come after the National Committee for Civil Defense earlier announced that four people had been killed. India's Meteorological Department called the Mekunu cyclone as extremely severe.
Socotra's governor Ramzy Mahrous said on Sunday that the death toll on the island remained seven - five Yemenis and two Indian sailors.
In Salalah, the heavy rain had nearly stopped on Saturday, an AFP photographer said, but many streets were still under water and nearby valleys were flooded.
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The Yemeni high relief agency met with global humanitarian organizations in Aden late Thursday to discuss the situation, the country's Saba news agency reported.
The maximum speed of the storm was 170-180 kilometers per hour and gusts were up to 200 kph.
The airport, closed since Thursday, was set to reopen on Sunday, Oman's Public Authority for Civil Aviation said. Over 230 families in Oman have been relocated to better buildings.
Salalah Port Services said it would take a minimum of 72 hours to "make the port safe".
"It was a scary feeling, as if it was the end of world", Mohammed Omer Baomer, an Omani resident, told AP. "You try to watch from the window and you can't". At one luxury hotel in Salalah, which already had evacuated its guests, workers sat down early for "suhoor", a meal Muslims eat before sunrise during the holy fasting month of Ramadan.