Parts of South Korea have seen 44 consecutive days of rain, the longest monsoon since 2013, and continued showers across the Korean peninsula are threatening to bring new floods and landslides.

In a visit to one of the hardest-hit areas, near the border with North Korea, Moon expressed regret about a North Korean move earlier in the week to suddenly release excess water from a dam without notifying the South.

While no specific damage from the release was reported and it was unrelated to the rescue accident, Moon said the unexpected rush of water had made it more difficult for South Korean authorities to manage already swollen rivers.

Heavy rain has also fallen in North Korea and state media published pictures of flooded streets but did not give any detail of damage or casualties.

The government in North Korea had issued a flood alert for areas near some its biggest rivers and lakes, the Rodong Sinmun newspaper reported.

South Korean Prime Minister Chung Sye-kyun, meanwhile, visited a river near the city of Chuncheon, to the northeast of Seoul, where more than 800 police and fire officials using seven helicopters and 69 boats were searching for the missing rescue workers.

Two rescue boats were trying to free a police boat stuck in wire by a dam near Chuncheon when they overturned, Yonhap news agency reported.

One man was rescued at the scene but seven others were swept over the dam's floodgates.

One of the seven, a 68-year-old man, was found near the dam suffering from cardiac arrest but was recovering. Another, also 68, was recovered dead about 20km downstream, Yonhap reported.

Elsewhere in South Korea, at least 16 people have been killed and 11 are missing, with more than 1600 people displaced over recent days.

Australian Associated Press