Seoul also called on its neighbour to give prior warning the next time it releases dam water.
More than 1,000 rescue workers were mobilised on Monday to search for the missing campers.
Police are also investigating whether there was any negligence by South Korean officials in charge of issuing flood alerts.
In addition to the missing South Koreans, police found the body of a boy aged four or five who apparently drifted downstream from the North on Sunday.
His death is believed to be related to the same incident.
|Thousands of rescue workers have been mobilised to find the missing campers [AFP]
The South's ruling Grand National Party demanded an apology for the water discharge.
"Whatever the reason was, it was an unpardonable criminal act," the party said in a statement.
"North Korea must make an immediate and official apology over the incident and present countermeasures to prevent it from recurring."
The incident comes as inter-Korean relations were improving after more than a year of tensions.
Last month, the North freed five South Korean detainees, eased border curbs, and sent envoys for talks with Lee Myung-bak, the president.
The North began building dams on the river in 2000, and previously unannounced water discharges aimed at generating electricity have damaged fish farms and riverside areas in Yeoncheon County, located 60km north of Seoul.
Sunday's incident was the first to claim any lives.