Speaking at a cabinet meeting on Tuesday, Lee ordered officials to take necessary measures to protect the daily lives of people and inspect power systems as demand for air-conditioning surges.
"An even greater concern is that abnormal weather conditions make it highly likely that extreme weather will continue for a considerable period," said Lee, who wants a major redesign of the disaster response system to cope with the hazardous conditions.
The nation's weather agency said Yangsan, a southeastern inland city sitting in a basin, recorded a temperature of 42.5C on Sunday, the highest temperature measured in 122 years of weather observations.
The Korea Meteorological Administration also issued its first-ever heatwave warning for parts of Seoul and neighbouring Gyeonggi on Monday, extending this to all of the capital on Tuesday.
A heatwave alert advises people to suspend outdoor activities such as farming, sports and work on construction sites.
"I have never felt heat like this so far here," said Cho Sang-yeon, who has lived for nearly 20 years in a jjokbang village, an area of cheaper single-room housing in western Seoul's Yeongdeungpo district.
Some residents have been moved to government-provided temporary housing equipped with air-conditioning, though many homeless people also live in the area.
Firefighters and other officials had been spraying water on roads in the area and checking on vulnerable residents for heat-related illnesses, said Jun Hong-cheol, an official at Yeongdeungpo Fire Station.
The Korea Disease Control and Prevention Agency said the death toll from the heatwave has risen to 19, including 13 people aged 80 or above.
Since May 15, 2025, people have suffered heat-related illnesses nationwide, according to data from the weather agency.
Two baseball games scheduled for Tuesday in Seoul and Gwangju were cancelled because of the extreme heat.