Japan's prime minister, Shinzo Abe, has promised to act quickly to address the buildup of huge quantities of contaminated water at the Fukushima Daiichi nuclear power plant.

Abe, who recently suggested that the plant's operator, Tokyo Electric Power (Tepco), was incapable of overseeing the operation on its own, said the government would soon announce a comprehensive plan to deal with the world's largest nuclear cleanup.

The prospect of greater state involvement in decommissioning Fukushima Daiichi – the scene of a triple meltdown after it was hit by a tsunami in March 2011 – comes amid growing concern that Tepco is ill-equipped to cope with the scale and complexity of the cleanup.

Those doubts were fuelled by evidence that the plant is seeping up to 300 tonnes of contaminated water into the Pacific Ocean every day. In a separate incident, a water storage tank was found to have leaked about 300 tonnes of highly toxic water, some of which could have found its way into the sea.

At the weekend, radiation near another tank was measured at 1,800 millisieverts an hour – a level that could kill an unprotected person in just four hours – and 18 times higher than previously thought.

Tepco had initially recorded radiation near the tank at about 100 millisieverts an hour, but admitted that this was because the equipment used could only read measurements up to that level. The latest reading came from a more advanced device capable of reading up to 10,000 millisieverts.

The buildup of water at the site is close to becoming unmanageable. Experts say that Tepco will soon be left with no choice but to release the water into the ocean or evaporate it.

At present, water is used to cool melted nuclear fuel in three reactor basements, where it becomes contaminated and then mixes with groundwater seeping down from the hills behind the plant. The site's tanks, basements and pits contain an estimated 338,000 tonnes of tainted water.

The chairman of the country's nuclear regulation authority, Shunichi Tanaka, said on Monday that discharging the water remained an option, but only after it had been treated to bring radiation levels to below regulatory limits.

"If we decide to discharge water into the ocean, we will use various methods to ensure that radiation is below accepted levels," Tanaka told reporters in Tokyo. "We will have to dispose of it eventually, but we are committed to reducing or removing radioactive materials.

"There are specific limits that are used worldwide for the discharge of contaminated water. Nuclear power plants do that under normal circumstances – we're not asking for an exception to be made in Fukushima's case."

Tanaka said monitoring of the more than 1,000 water tanks at the site had been "inadequate". Previously, only two workers were dispatched twice a day to check the tanks, but did not carry personal radiation monitors and failed to keep proper records of their inspections. Tanaka said that a small leak and signs of possible leaks had been spotted at several other storage tanks.

Tepco apologised for the "great anxiety and inconvenience" caused by the contaminated water.

But the utility took issue with media reports suggesting workers at the site were at risk of being irradiated.

Most of the radiation in the most recent incident – measured at 1,800 millisieverts an hour – was emitted in the form of beta rays, it said. Beta radiation travels only a short distance and can be blocked by a thin sheet of metal, such as aluminium, it added.

"We believe that we can control radiation exposure by the using proper equipment and clothing," the firm said in an emailed statement. "We will investigate the cause of this issue, taking any appropriate countermeasures immediately, and continue to make every effort to secure the safety of workers."

The government is expected to unveil emergency measures on Tuesday to deal with the water crisis. The plan will include steps to prevent a further buildup of contaminated water, possibly financed by the state, media reports said.

Abe has come under pressure from his party's coalition partner to intervene at Fukushima Daiichi. The toxic water leaks were "very serious", Kyodo quoted New Komeito's leader, Natsuo Yamaguchi, as telling Abe at a meeting on Monday. "I want the government to deal with the problem in a comprehensive manner."

The leaks threaten to delay Abe's plans to restart nuclear reactors, a move he says is necessary to support Japan's economic recovery and improve Tepco's tattered finances.

Of Japan's 50 working nuclear reactors, only two are in operation. One of those was to be shut down on Monday evening to undergo routine checks, the other will go offline on 15 September, leaving Japan without atomic energy for only the second time in almost 50 years.

Concern is growing that the stream of bad news from Fukushima could threaten Tokyo's bid to host the 2020 Olympics. The International Olympic Committee will announce the host city – the two other candidates are Madrid and Istanbul – in Buenos Aires on Saturday.

Japan's foreign ministry has started posting English-language information online showing that atmospheric radiation levels in Tokyo, 140 miles south of Fukushima Daiichi, are comparable with those in London and New York.