Mekunu battered the southern coast of Oman and killed at least two people before downgrading to a deep depression, authorities said.
Thousands of people living near coastal areas in Dhofar and al-Wusta had been moved to shelters as 170km/h (105mph) winds and torrential rain hammered the region, officials said.
Considering the course it has followed till now, the Cyclone Mekunu is expected to make landfall near Salalah Friday-Saturday midnight which is Oman's third-largest city and inhabits about 200,000 people close to the kingdom's border with Yemen.
Al Jazeera's Mohamed Vall reporting from Salalah in Oman said that many drivers were caught unaware and had to contend with rapidly rising waters.
Late Saturday it struck Saudi Arabia's Empty Quarter, one of the world's most arid deserts, with ongoing heavy rains and strong winds.
The cyclone is marching onwards straight towards the south coast of Oman.
Mekunu started to weaken to a tropical storm in Oman and authorities began clearing operations on Saturday after the heavy rain but warned residents to stay in their homes, with run-off from river valleys flooding most main roads in Dhofar.More news: Suspect in Custody After Shooting at Indiana Middle School
The company said its preliminary assessment suggested damage was not severe, but added that the "total impact of the cyclone on plant operations can not yet be precisely assessed".
The meeting also discussed measures to provide aid to residents of three provinces in southeast Yemen expected to be hit by the cyclone. They described the cyclone as "extremely severe".
The internationally recognised government of President Abedrabbo Mansour Hadi declared early Thursday Socotra a "disaster province" due to severe damage, according to Saba.
The authorities are closely monitoring the weather conditions and it is likely to be partly cloudy and hazy.
Tropical Cyclone Mekunu left behind death and destruction after sweeping through waters near Yemen's southern island of Socotra and pounding the island, a local official said Friday.
In 2007, Cyclone Gonu tore through Oman and later even reached Iran, causing $4 billion in damage in Oman alone and killing over 70 people across the Mideast.