* Voters want coalition for better disaster handling
* More bodies recovered from tsunami-hit coast
* Damages bill could top $300 billion
* Business sentiment turns negative after disaster
By Chizu Nomiyama and Yoko Nishikawa
TOKYO, April 4 (Reuters) - Japanese engineers put dye into radioactive water on Monday to check if they had managed to stop a leak from one reactor at the crippled Fukushima nuclear plant but one official warned it would be months before the crisis was under control.
In the face of Japan's biggest crisis since World War Two, one newspaper poll said that nearly two-thirds of voters want the government to form a coalition with the major opposition party and work together to recover from the massive damage from the March 11 earthquake and tsunami.
Underlining the concern over the impact on the world's third largest economy, a central bank survey showed that big manufacturers expect business conditions to worsen significantly in the next three months, though they were not quite as pessimistic as some analysts had expected. [ID:L3E7F4006]
An aide to embattled Prime Minister Naoto Kan said on Sunday that the government's priority now was to stop radiation leaks from the Fukushima nuclear plant, 240 km (150 miles) north of Tokyo, and that the situation had "somewhat stabilised".
"How long will it take to achieve (the goal of stopping the radiation leaks)? I think several months would be one target," said Goshi Hosono, a ruling party lawmaker and aide to Kan.
Engineers at plant operator Tokyo Electric Power Co (TEPCO) have been scrambling to find anything that will help stop the leaks and prevent reactors from overheating.
They mixed sawdust and newspapers with polymers and cement to try to seal a crack in a concrete pit at reactor no.2, where radioactive water has been seeping into the sea.
"We were hoping the polymers would function like diapers but are yet to see a visible effect," said Hidehiko Nishiyama, a deputy director general of the Nuclear and Industrial Safety Agency.
Nishiyama said three of the six reactors were now generally stable. TEPCO has said it will scrap at least four reactors once they are under control, but this could take years or even decades.
Japan's crisis has rocked the nuclear industry and the European Union said on Sunday it will affect the fight against climate change as energy policies are reviewed. [ID:nL3E7F3049]
Germany and Switzerland have said they will shut older reactors or suspend approvals, China has suspended approvals for new plants, and Taiwan is studying cutting nuclear output.
Japan may review its pledge to cut its 2020 greenhouse gas emissions by 25 percent from 1990 levels in the wake of the Fukushima nuclear power plant crisis, Japanese media quoted a senior environment ministry official as saying.
"It is true that our reduction target will be affected significantly," Hideki Minamikawa, vice minister for global environmental affairs, was quoted by the Yomiuri newspaper as saying. [ID:L3E7F30F3]
PM UNDER PRESSURE
The 9.0 magnitude quake and tsunami left nearly 28,000 people dead or missing and Japan's northeast coast a splintered wreck. The disaster has hit economic production and left a damages bill which may top $300 billion.
Prime Minister Kan is under intense pressure to steer Japan through the crisis, but after three weeks many Japanese are angry the humanitarian disaster seems to have taken a back seat to the nuclear crisis.
Though criticised for his crisis management, voter support for Kan's government rose to 31 percent in a Yomiuri newspaper poll, from 24 percent in a survey conducted before the quake.
Almost 70 percent of respondents, however, believed Kan was not exercising leadership, 19 percent wanting him to step down soon.
There has been talk that Kan's ruling Democratic Party of Japan join forces with its main political opponent, the Liberal Democratic Party (LDP). But so far there has been no sign the two are close to any deal.
Kan last month invited LDP head Sadakazu Tanigaki to join the cabinet as deputy premier for disaster relief, but he declined.
MOVES TO STOP POWER BLACKOUTS
More than 163,710 people are living in shelters, with more than 70,000 people evacuated from a 20 km (12 mile) no-go zone area the nuclear plant. Another 136,000 people living a further 10 km out have been told to leave or stay indoors.
The government estimates damage from the earthquake and tsunami at 16 trillion to 25 trillion yen ($190 billion-$298 billion). The top estimate would make it the world's costliest natural disaster.
Manufacturing has slumped to a two-year low as a result of power outages and quake damage hitting supply chains and production.
The Bank of Japan's tankan business sentiment survey, although negative, was not as grim as analysts had expected, With some suggesting the results were not reliable.
"I think many firms will have filled out the surveys before the quake and sent them after the quake, so this reading may be misleading to gauge the impact of the quake," said Masamichi Adachi, senior economist at JPMorgan Securities Japan.
General Electric , which helped build the Fukushima Daiichi nuclear power plant will help TEPCO supply electricity in the coming months when demand soars. [ID:nL3E7F304N]
Demand for power jumps in Japan in summer due to heavy use of air conditioners. More than 168,500 households in the north are still without electricity after the tsunami.
The government has said it will restrict maximum power use by companies during the hotter months in an effort to avoid further blackouts.
Japan's health ministry said on Sunday it had detected radioactive substances higher than legal limits in mushrooms from Iwaki in Fukushima, said Kyodo.
"Grown in Fukushima" has become a warning label for those nervous of radiation which has already been found in some vegetables close to the nuclear plant. (Additional reporting by Shinichi Saoshiro, Kiyoshi Takenaka and Yoko Kubota in in Tokyo, David Fogarty in Bangkok; Writing by Paul Eckert and Jonathan Thatcher; Editing by Andrew Marshall)