* Cracked pit possible source of radiation leak
* Japan PM visits tsunami-hit village, enters rector zone
* Nuclear crisis enters fourth week, no quick solution (Adds new measure to stop leak, latest figure for dead, missing)
By Kiyoshi Takenaka and Chisa Fujioka
TOKYO, April 3 (Reuters) - Japanese officials grappling on Sunday to end the world's worst nuclear crisis since Chernobyl were focusing on a crack in a concrete pit that was leaking radiation into the ocean from a crippled reactor.
Tokyo Electric Power Co (TEPCO) <9501.T> said it had found a crack in the pit at its No.2 reactor in Fukushima, generating readings 1,000 millisieverts of radiation per hour in the air inside the pit. [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), said on Saturday.
He cautioned, however: "We can't really say for certain until we've studied the results."
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Leakage did not stop even after concrete was poured into the pit, and Tokyo Electric is now planning to use water-absorbent polymer to prevent contaminated water from leaking out into the sea.
Officials from the utility said checks of the other five reactors found no cracks.
Nishiyama said that to cool the damaged reactor, NISA was looking at alternatives to pumping in water, including an improvised air conditioning system, spraying the reactor fuel rods with vaporized water or using the plant's cleaning system.
PM UNDER PRESSURE
As the disaster that has left more than 27,000 dead or missing dragged into a fourth week, Prime Minister Naoto Kan toured devastated coastal towns in northern Japan on Saturday, offering refugees government support for rebuilding homes and livelihoods.
"It will be kind of a long battle, but the government will be working hard together with you until the end," Kyodo news agency quoted him as telling people in a shelter in Rikuzentakata, a fishing port flattened by the tsunami which struck on March 11 after a massive earthquake.
Unpopular and under pressure to quit or call a snap poll before the disaster, Kan has been criticised for his management of the humanitarian and nuclear crisis. Some tsunami survivors said he came to visit them too late.
Kan also 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.
Operators of the plant are no closer to regaining control of damaged reactors, as fuel rods remain overheated and high levels of radiation are flowing into the sea.
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 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.
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. (Additional reporting by Chizu Nomiyama, Yoko Kubota, Shinichi Saoshiro in Tokyo and Damir Sagolj in Rikuzentakata; Writing by Paul Eckert; Editing by Jeremy Laurence)