Cyclone Shaheen made landfall in Oman on Sunday. The arrival of the storm led to high gust winds and heavy rainfall in the country.
Authorities urged residents to evacuate coastal areas and delayed flights to and from the capital, Muscat
A child who had been swept away by water was found dead, the state news agency said. Another person is missing. Two Asian workers were killed when a hill collapsed on their housing area in an industrial zone as a result of the cyclone.
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More than 2,700 people have been put up in emergency shelters.
Most of the oil-exporting country's five million people live in and around Muscat. Authorities said roads in the capital would be open only to vehicles on emergency and humanitarian journeys until the storm dies down.
Police officials are conducting security patrols near beaches and valleys where torrential rains were expected
The national emergency committee has said the power supply would be cut to avoid accidents.