But Japan's Nuclear Regulation Authority proposes elevating it to level three on the seven-point scale.
Japanese reports say it is a provisional move that had to be confirmed with the IAEA, the UN's nuclear agency.
This week is the first time that Japan has declared an event on the Ines scale since the 2011 earthquake and tsunami.
The move was announced in a document on the agency's website and was subsequently approved at a weekly meeting of the regulatory body.
The March 2011 tsunami knocked out cooling systems to the reactors at the plant, three of which melted down.
Water is now being pumped in to cool the reactors but this means that a large amount of contaminated water has to be stored on site.
There have been leaks of water in the past but this one is being seen as the most serious to date, because of the volume - 300 tons of radioactive water, according to Tepco - and high levels of radioactivity in the water.
Japan's Nuclear Regulation Authority (NRA) said it feared the disaster was "in some respects" beyond Tepco's ability to cope.
"We should assume that what has happened once could happen again, and prepare for more," watchdog chairman Shunichi Tanaka told a news conference. "We are in a situation where there is no time to waste."
He said Tepco had failed to spot the leak for days - maybe weeks - despite patrols that are supposed to check each storage tank twice every day. Workers had also left a tap open in the safety barrier that surrounds the base of the leaking storage tank.
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