Subway stations and major roads have been underwater in the South Korean capital Seoul after record-breaking rains caused severe flooding that left at least seven people dead.

At least five people died in Seoul and two others in the neighbouring Gyeonggi Province by early Tuesday, the Central Disaster and Safety Countermeasures Headquarters said.

Four died after being trapped in flooded buildings, one was believed to have been electrocuted, one person was found under the wreckage of a bus stop, and another died in a landslide, it said.

At least nine people were injured, while six were missing.

The headquarters raised the crisis alert to the highest and requested organisations adjust their working hours.

The downpour that began on Monday is the heaviest rainfall in South Korea in 80 years, according to Seoul's Yonhap News Agency. 

Authorities warned of more rain to come even as emergency workers tried to clear the hulks of flooded cars, which were strewn across major intersections throughout the city.

Gangnam, a wealthy district in southern Seoul — which was featured in Psy's 2012 K-pop hit "Gangnam Style" — received 326.5 millimetres of rainfall on Monday, data from the Korea Meteorological Administration showed.

President Yoon Suk-yeol ordered government officials to evacuate residents from high-risk areas and encouraged businesses to allow employees flexible commuting hours on Tuesday morning.

"Record-breaking torrential downpours in the central region since yesterday have caused a lot of damage, including unfortunate casualties," Yoon said on Facebook Tuesday, adding the government would provide "prompt recovery and damage support".

Nearly 800 buildings in Seoul and nearby cities were damaged while at least 790 people were forced to evacuate from their homes, the Ministry of the Interior and Safety said.

The Korea Meteorological Administration warned South Koreans to "be careful of the heavy rain, gusts, as well as thunder and lightning in the central region" for the next few days.

The country’s weather agency maintained a heavy rain warning for the Seoul metropolitan area and nearby regions on Tuesday and said the precipitation may reach 5-10 centimetres an hour in some areas. 

It said around 10 to 35 centimetres of more rain was expected across the capital region through Thursday.

Power outages were reported across the capital late on Monday, while some operation of the Seoul metro and railway services was temporarily disrupted by the heavy rain.

The Seoul express bus terminal in Gangnam was submerged, and flood water also leaked into a cafe and library at the COEX Convention and Exhibition Center in the same area.

South Korea remained highly disrupted on Tuesday, with many roads and tunnels closed for safety reasons, Yonhap reported.