TOKYO—Japanese officials continued their battle to control dangerous reactor overheating in the nation’s worst nuclear accident that followed Friday’s earthquake, as they resorted to an unprecedented attempt to cool the reactor with seawater.

Japan Chief Government Spokesman Yukio Edano said Sunday that work is continuing on attempts to shut down two nuclear reactors at Tokyo Electric Power Co.’s Fukushima Daiichi power plant in northern Japan.

Mr. Edano acknowledged that radiation levels have risen at the plant as venting of slightly radioactive steam continues in a bid to lower pressure in the container vessel and allow the pumping of cooling water. . .