Eyewitnesses likened the conditions to being on a battlefield.
Hundreds of domestic and international flights have been cancelled due to continuing heavy rain and strong winds.
Officials said Nari, named after a South Korean flower, was moving northeast at 26 kilometres per hour toward the Korea Strait between the peninsula and Japan.
The agency also predicted heavy rainfall in Gangwon, as well as in South and North Gyeongsang provinces along the country's east coast.
Taiwan meanwhile has issued a sea warning for ships traveling through its northern and eastern waters on Monday as tropical storm Wipha approached the island packing winds of 108 kmh.
If Wipha stays at its current course, the fringe of the storm could affect the island on Tuesday morning, forecasters said.