* Average productivity cut to 2.97 T per hectare
* Record corn crop forecast of 76.1 mln T maintained
* Yields seen improving in Rio Grande do Sul (Adds CBOT prices, quote from farmer)
SAO PAULO, March 7 (Reuters) - Brazil's government cut 1.3 million tonnes, or 1.6 percent, off its forecast for the 2012/13 soybean crop on Thursday, citing too little rain in parts of the south in January and too much rain in the top soy state Mato Grosso in February.
Brazil is still expected to produce a record soy crop of 82.1 million tonnes, a huge increase from last season's 66.4 million tonnes, but less than the 83.4 million tonnes previously forecast by Conab, Brazil's crop supply agency, in February.
"The reason for the decrease is adverse climate conditions, like excess rain in the center-west and drought in parts of the south," Conab said in an e-mailed statement.
The agency, however, held its forecast for soybeans available for export at 36.78 million tonnes. They are needed to replenish low global stocks after drought hurt crops in both Brazil and the United States last season.
Conab's forecast is now equal to the U.S. Department of Agriculture's estimate for U.S. soybean output, which will be revised on Friday. Brazil had been expected to surpass the United States as the world's top soybean producer this season after its area planted with soy expanded by 10.4 percent.
But as Brazil's harvest approaches the half-way mark, Conab lowered its yield expectations. The agency forecast average productivity in Brazil's fields at 2.968 tonnes per hectare, less than the 3.02 tonnes per hectare estimated in February.
Yields are seen highest in Parana, the No. 2 soybean producing state, at 3.26 tonnes per hectare and lowest in the tiny state of Piaui, at just 2.34 tonnes per hectare. The worst drought in decades in Northeastern Brazil hurt producers in the frontier agricultural region this season.
Producers in Rio Grande do Sul, Brazil's No. 3 soy state where the harvest is just starting, said the lack of rain in January was concerning, though better weather in February should improve yields for beans gathered later on.
"Some soy went 26 days without rain, the first beans to be harvested suffered the most, but 70 percent of the crop had a normal development," said Lisandro Webber, a farmer in Passo Fundo, Rio Grande do Sul.
Analysts have emphasized yields that vary widely across the state.
March soybean contracts already in delivery rose 0.91 percent on the Chicago Board of Trade while May beans were up 0.27 percent.
In its sixth official forecast, Conab also said it expected a record corn crop of 76.1 million tonnes, unchanged from its February outlook.
If achieved, that would be more than last season's record 72.7 million-tonne crop, but the majority of the corn, 40.9 million tonnes, will be planted after the main soy crop is harvested and will not be available until May, Conab said.
The agency maintained its February forecast of 4.3 million tonnes of wheat this season in Brazil, which is looking to import more of the grain from the northern hemisphere after a slim crop in Argentina, its main supplier.
Brazil, an agricultural powerhouse that is poised to take on a larger share of the world's food production in coming years, will also produce a cotton lint crop of 1.4 million tonnes, down from 1.9 million tonnes last year, Conab said. (Reporting by Caroline Stauffer in Sao Paulo and Gustavo Bonato in Rio Grande do Sul; Editing by Chizu Nomiyama and Marguerita Choy)