The authority proposed raising the leak threat from a level 1 on an international scale to a level 3, The Japan Times reported.
The International Nuclear and Radiological Event Scale defines a level 3 rating as a "serious accident" while a level 1 designation means an "anomaly."
Approximately 300 tons of highly radioactive water has leaked from tank No. 5 at the damaged plant so far.
NRA chief Shunichi Tanaka said the plant has some 1,060 tanks containing highly radioactive water that would be released at once if another tsunami came along.
The authority plans to consult with the International Atomic Energy Agency to determine if its severity level assessment is appropriate since the leak occurred in the wake of a meltdown crisis that was already classified as a level 7 or "major accident."
INES ratings are usually applied after accidents at undamaged nuclear-related facilities.