Dhofar and Al Wusta provinces on Friday after intensifying from a category one to a category two cyclone, with winds of up to 170 kilometres per hour after it made landfall on Socotra on Thursday.
The meteorology department said the latest weather charts and satellite imageries indicate that Mekunu's intensity has dropped to "a deep depression".
The civil defence teams had also rescued dozens of people who were trapped because of floods.
Alongside loss of life, damage has been severe, as Mekunu slammed into several popular urban and tourist destinations along the Arabian Sea, with flash flooding destroying entire roadways in Oman's third-largest city of Salalah.
The central bank, meanwhile, issued a circular announcing a three-day holiday starting on Sunday for money exchange houses, banks, finance and leasing companies in Dhofar.
Strong winds knocked over street lights and tore away roofing.
Salah is home to about 2,00,000 people and portion of it lost power after being hit by the storm. The beaches were littered with debris. The cyclone has been wreaking havoc on the Yemeni island of Socotra from the past two days.
Fast-moving waters from the rain and storm surge flooded normally dry creek beds.
An Asian laborer died in a flooded valley and an Omani national in a 4×4 died when his vehicle was swept away, al-Shanfari said.
Now it is known about two dead in Yemen and four in Oman, including a 12-year-old girl and an Asian immigrant.
Communication lines and water services have also been taken down by the winds.
Socotra Governor Ramzy Mahrous said one ship sank and two others ran aground in the storm, initially saying authorities believed 17 people were missing and presumed dead.