High levels of radioactivity in water leaking from a reactor at the Fukushima Daiichi nuclear power plant resulted from a partial meltdown of fuel rods, Japanese officials have said, amid growing fears that radiation may also have seeped into seawater and soil.

Contamination in a pool of water in the turbine building of the No 2 reactor was found to be 100,000 times normal levels, the plant's operator, Tokyo Electric Power (Tepco), said.

On Sunday the firm said the figure was 10m times higher, a mistake the government's chief spokesman, Yukio Edano, said was "absolutely unforgivable".

Tepco was forced into another embarrassing apology after it admitted it had twice named the wrong isotope in its corrections about the levels of radiation.

"On one hand, I do think the workers at the site are getting quite tired," Edano told reporters.

"But these radiation tests are being used for making various decisions on safety … they are absolutely unforgivable."

In addition, radiation above 1,000 millisieverts per hour was found in surface water in trenches outside the No 2 reactor, Tepco said. It added that the trenches did not lead to the sea, but conceded it could not rule out that radioactive water had seeped into the ground.

Greenpeace, meanwhile, said that it had recorded radiation levels of up to 10 microsieverts per hour in Iitate, a village 25 miles from the plant, and urged authorities to expand the evacuation zone from its current 12-mile radius.

"It is clearly not safe for people to remain in Iitate, especially children and pregnant women, when it could mean receiving the maximum-allowed dose of radiation in only a few days," said Jan van de Putte, the group's radiation safety expert. "When further contamination from possible ingestion or inhalation of radioactive particles is factored in, the risks are even higher."

In a sign that Tepco is struggling to regain control of the reactors, it has reportedly asked the French nuclear sector for assistance. Tepco has sought help from Electricité de France, Areva and the Nuclear Energy Agency, a research body, Eric Besson, France's industry and energy minister, said.

Japan's nuclear and industrial safety agency (Nisa) said radioactive iodine-131 of 1,150 times the maximum allowable level had been detected in seawater near drainage outlets serving four of Fukushima's reactors.

Nisa spokesman Hidehiko Nishiyama said he suspected radioactive water from the plant was leaking into the sea. On Sunday he had denied any connection between the two.

Edano said that partial meltdown had probably occurred when the plant was hit by the 11 March tsunami, adding that there was no evidence of subsequent meltdown.

Four of the facility's six reactors are yet to be made safe, while efforts are continuing to pump in fresh water to prevent a far more dangerous full meltdown.

"The radiation seems to have come from fuel rods that were partially melted down and came into contact with the water used to cool the reactor," Edano said. "Steam may have condensed … carrying water from within the containment vessel."

Airborne radiation has been confined to the reactor buildings , and work to remove contaminated water from the structures continued on Monday.

Recent setbacks to attempts to cool the reactors, and the realisation the crisis is far from over, have added to the plight of tens of thousands of people living nearby.

Sakae Muto, vice-president of Tepco, said: "Regrettably, we don't have a concrete schedule at the moment to enable us to say how many months, or years it will take [to make the plant safe]."

About 70,000 people within a 12-mile radius of the Fukushima plant were evacuated soon after the disaster, while a further 130,000 people living in a 12-20-mile radius have been told to stay indoors.

The government said that it had no plans to widen the evacuation zone.

Fukushima prefecture authorities do not have any exact figures on how many people remain in the 12.7-18.6 miles rradius. Many have left voluntarily after days of living without essential supplies and services.

Media reports say that many truck drivers are refusing to enter the zone, fearing radiation exposure.

The government created confusion last week when it advised people within a 20-mile radius to consider leaving the area. It insisted the advice was given due to concern for their quality of life, not exposure to harmful levels of radiation.

According to the public broadcaster NHK, self-defence force personnel in the evacuation zone said 30 people had yet to leave the 12-mile evacuation zone, and 10 had indicated they wanted to remain in their homes.

Evacuees have been urged not to return to the area to collect belongings while the Fukushima plant remains unstable. Residents who return, even temporarily, would expose themselves to "great risk of radiation contamination", Edano said.

"It is very likely that the 20km area is contaminated and there is a significant risk to health," he added. Local authorities reported, however, that some people had already returned.

Others forced out of their homes are coming to terms with the possibility that they may never be able to return.

Even if they do, the many residents who depended on Tepco for employment accept that with the plant ruined, their chances of finding work in the area are close to nil.

A large number of evacuees have already moved twice since the nuclear crisis began, and could be forced to move on again if the situation worsens and the evacuation zone is expanded.

"We're assuming that in a worse-case scenario we might also be subject to evacuation," Norio Hattori, a disaster official in Nihonmatsu, said, adding that he had sent his own daughter to Tokyo.

Some of the refugees are already beginning to accept that a vast area surrounding the Fukushima plant could be condemned as a nuclear wasteland.

"If it had been an earthquake or a tsunami, we could have gone home again, but because it's radiation, we can't," said Tokuko Sujimoto.

Her home, in the village of Namie, was so close to the plant she heard the first reactor explosion on 12 March.

She said that her husband had watched from the roof of their house as a cloud of smoke rose from the reactor, before the couple decided to flee.

Yoshimoto Nogi, who had a job at the Fukushima plant until he retired last summer, said he had no hopes of going home this year.

"It's going to take a year or two. It is not a question of months," said Nogi. "Even if the nuclear plant is stabilised tomorrow, I don't think the government is going to tell us it is safe to go back any time soon."