Tokyo Electric Power Company (Tepco) said on Tuesday the leak was believed to be continuing at Fukushima and that it had not yet pinpointed the source of it.
Tepco said puddles with extremely high radiation levels have been found near the water tanks at the plant.
The radiation level was about 100 millisieverts per hour, it said.
"This means you are exposed to the level of radiation in an hour that a nuclear plant worker is allowed to be exposed to in five years," a Tepco official told reporters.
The company later said it had identified which tank was leaking but had yet to find the spot from where it was leaking.
"We have instructed Tepco to find the source of contaminated water … and to seal the leakage point," an official from the Nuclear Regulation Authority said.
"We have also instructed them to retrieve contaminated soil to avoid a further expansion of toxic water, and to strengthen monitoring of the surrounding environment."
There were no significant changes in radiation levels outside the plant, he added.
Could contaminate groundwater
Tepco admitted it was possible the toxic water could contaminate groundwater and flow into the Pacific Ocean "in the longer term", but said it was working to avoid such a situation.
"We are transferring the contaminated water from a tank with a leakage problem to unbroken tanks, and retrieving leaked water and soil around it," the Tepco official said.
"We are also beefing up existing earth-fill dams around tanks," he said, as the region braces for heavy rain later on Tuesday.
So far four tonnes of the spilled water had been retrieved since Monday evening when Tepco started the recovery operation, the company said.
Tepco has faced a growing catalogue of incidents at the plant including several leaks of radioactive water, more than two years after the worst nuclear disaster in a generation triggered by a huge quake and tsunami in March 2011.
The company – which faces huge clean-up and compensation costs – has struggled with a massive amount of radioactive water accumulating as a result of continuing water injections to cool reactors.
Cleanup at Fukushima
The embattled utility in July admitted for the first time that radioactive groundwater had been leaking outside the plant. This month it started pumping it out to reduce leakage into the Pacific.
The problems have led the Japanese government and its nuclear regulator to say they would get more directly involved in the cleanup at Fukushima.
While no one is officially recorded as having died as a direct result of the meltdowns of Fukushima's reactors, large areas around the plant had to be evacuated.
Tens of thousands of people are still unable to return to their homes. – AFP