* Japan PM visits tsunami-hit village, enters nuclear zone
* Nuclear crisis enters fourth week, no quick solution
* IMF warns economy to be hit by quake, possible yen intervention
* Cracked concrete pit might be source of radiation leak (Adds report that leak has not been stopped, para 5)
By Kiyoshi Takenaka and Chisa Fujioka
TOKYO, April 2 (Reuters) - Japan's prime minister made his first visit to the country's tsunami-devastated region on Saturday as officials grappling to end the worst nuclear crisis since Chernobyl said they may have discovered why radiation has been leaking into the sea.
Tokyo Electric Power Co (TEPCO) <9501.T> said it had found a crack in a concrete pit that was leaking water at its No.2 reactor in Fukushima, measuring 1,000 millisieverts of radiation per hour. [ID:nL3E7F2039]
"With radiation levels rising in the seawater near the plant, we have been trying to confirm the reason why, and in that context, this could be one source," said Hidehiko Nishiyama, deputy head of the Nuclear and Industrial Safety Agency (NISA).
He cautioned, however: "We can't really say for certain until we've studied the results."
TEPCO poured concrete into the pit to stop the leak, but water prevented it from hardening and the leak had yet to be stopped, public broadcaster NHK said.
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Prime Minister Naoto Kan spoke with refugees living in a makeshift camp in the fishing village of Rikuzentakata, levelled by the tsunami which struck on March 11 when Japan was rocked by a massive earthquake, leaving 28,000 dead and missing.
"It will be kind of a long battle, but the government will be working hard together with you until the end. I want everyone to do their best, too," Kyodo news agency quoted Kan as telling one survivor in a school that is now an evacuation shelter by Japan's shattered northeast coast.
But some survivors were angry Kan took three weeks to visit, accusing the government of doing little to help them rebuild their lives amongst the twisted rubble.
"The timing of his visit is too late," said Ryoko Otsubo. "I wish he had visited this place earlier. I wanted him to see the piles of debris where there were no roads. Now the roads are cleaned."
Despite its tsunami seawalls, Rikuzentakata was flattened into a wasteland of mud and debris and many of its 23,000 residents killed or injured, some swept away by the waves.
"A person that used to have a house near the coast told me 'Where am I supposed to build a house after this?', so I encouraged this person and said the government will provide support until the end," Kan told reporters.
Unpopular and under pressure to quit or call a snap poll before the disaster, Kan has been criticised for his management of Japan's humanitarian and nuclear crisis and his leadership remains in question.
"There are some evacuation centres that lack electricity and water. There are people who can't even go look for the dead. I want him to pay attention to them," Kyodo quoted Kazuo Sato, a 45-year-old fisherman, as saying.
Kan later entered the 20-km (12-mile) evacuation zone and visited J-village just inside the zone, a sports facility serving as the headquarters for emergency teams trying to cool the six-reactor Fukushima Daiichi plant.
ECONOMIC CONSEQUENCES
After three weeks, operators of the plant are no closer to regaining control of damaged reactors, as fuel rods remain overheated and high levels of radiation flow into the sea.
TEPCO, Asia's largest power company, has seen its shares lose 80 percent -- $32 billion in market value -- since the disaster.
Japan is facing a damages bill which may top $300 billion -- the world's biggest from a natural disaster.
The International Monetary Fund (IMF) said on Friday the Japanese economy would take a short-term hit and it could not rule out further intervention for the yen. [ID:nEBE7DA00J]
The IMF is set to cut its 2011 forecast for Japanese growth when it unveils updated figures on April 11 in its World Economic Outlook, said IMF Japan mission chief Mahmood Pradhan.
Japan's central bank is expected to revise down its economic assessment when it meets on April 6-7 in the wake of the crisis.
The consequences for the world's third largest economy have already seen manufacturing slump to a two-year low. Power outages and quake damage have hit supply chains and production.
There has been growing talk of a coalition between the ruling Democratic Party of Japan and the main opposition Liberal Democratic Party (LDP) to tackle the aftermath of the crisis.
But there has been no agreement and the Yomiuri newspaper said some in the LDP would likely insist Kan step down first.
The government has already been battling the opposition to get laws in place to make the new budget, from April 1, workable.
Kan wants an extra budget soon for reconstruction which would also need help from opposition parties to function.
RADIATION BATTLE CONTINUES
Hundreds of thousands remain homeless, sheltering in evacuation centres, as the death toll from the disaster rises.
Thousands of Japanese and U.S. soldiers on Saturday conducted a search for bodies using dozens of ships and helicopters to sweep across land still under water along the northeast coast.
The teams hope when a large spring tide recedes it will make it easier to spot bodies.
Radiation 4,000 times the legal limit has been detected in seawater near the Daiichi plant and a floating tanker was to be towed to Fukushima to store contaminated seawater. But until the plant's internal cooling system is reconnected radiation will flow from the plant.
It could take years, possibly decades, to make safe the area around the plant, 240 km (150 miles) north of Tokyo.
With its president, Masataka Shimizu, in hospital, an enormous compensation bill looming and mounting criticism of both its handling of the crisis and prior safety preparations, TEPCO may need state help, according to media reports.
Kan has all but ruled out nationalising TEPCO but some sort of injection of public funds looks inevitable.
Standard & Poor's on Friday cut its long-term rating on TEPCO by three notches to "BBB+", in its second downgrade on the electric utility in as many weeks.
(Additional reporting by Terril Jones in Tokyo, Damir Sagolj in Rikuzentakata and Lesley Wroughton in Washington; Writing by Paul Eckert; Editing by Jonathan Thatcher and Jeremy Laurence)