A yellow alert in force until 5pm was issued on Monday by the met office, which said strong storms were likely in some areas
According to the warning, some areas could have rainfall exceeding 35 mm per hour.
The day started with dense fog in many parts of Cyprus, and police warned visibility was extremely limited, urging people to drive carefully and at low speed.
Temperatures are forecast to rise to 18C and drop to 7C in the evening in most areas. The top temperature in the mountains will be 9C and the lowest at night 3C.
On Tuesday, isolated rains will fall, with the weather gradually becoming more windy. For the night, the met office predicts rain, storms and snow in the mountains.
The conditions are going to improve by Wednesday afternoon, and according to the forecast on Thursday sunny weather will prevail.