Severe wet weather in South Korea eased on Monday following days of torrential rain that triggered floods and landslides and left at least 18 people dead, the Ministry of the Interior and Safety said on Monday.

Nine people remained missing as of Sunday evening, the ministry said, with residents of the worst-hit areas in shock.

At Gapyeong, some 62 kilometres (38.5 miles) northeast of the capital Seoul, some residents recalled narrow escapes from the floods after 173 millimetres (6.8 inches) of rain deluged the area over just 17 hours on Sunday.

Gapyeong was among a number of places that saw a record amount of rain in a single day and broke the previous high for national daily precipitation of 156.3 mm that was set on September 30, 1998.

"The ground just sank beneath me, and the water rose all the way up to my neck. Luckily, there was an iron pipe nearby. I held on to it with all my strength," said Ahn Gyeong-bun, the owner of a restaurant that was almost completely destroyed.

Two people died and four were missing after a landslide engulfed homes around Gapyeong and floods swept away vehicles as of Sunday, the ministry said.

For those remaining like Ahn, an uncertain future awaits.

"I've run this restaurant for 10 years ... What am I supposed to do now?" said Ahn, as she stood next to the badly damaged structure of her building perched next to a still swollen river.

At times breaking down in tears, the 65-year-old said several of the restaurant's refrigerators were washed away by the flood.

Across South Korea, rain damage had been reported to 1,999 public structures and 2,238 private facilities, including farms, the interior ministry said.

While the rain has eased, the national weather agency has now issued a nationwide heatwave watch.

South Korean President Lee Jae Myung has ordered a thorough response to the disaster, his office said.

"As local heavy rains have become commonplace, customised measures based on regional characteristics are urgently needed," said Kang Yu-jung, the spokesperson for Lee's office.

"If serious laxity or mistakes are found in civil servants' discipline, we will hold them accountable and thorough measures will be taken to prevent a recurrence."

Lee, who took office in June, has promised to make the country safer and to prevent any repeat of the disasters in recent years that have often been blamed on the inadequate response by authorities.