Brazil stocks dip despite Petrobras, real firms

*Stock market lower despite gains by Petrobras

*Real gain for third straight session

*Interest-rate futures fall on budget surplus optimism

SAO PAULO, May 13 (Reuters) - Brazil's main stock index fell slightly on Tuesday despite gains by market bellwether Petrobras, while the local currency firmed on expectations of increased dollar inflows.

The Bovespa index .BVSP of the Sao Paulo stock exchange was down 0.08 percent at 70,363.00 points after briefly touching an intraday record of 71,084.38 early in the session. Gains by state oil giant Petrobras, the heaviest weighted stock in the index, helped prevent the market from falling further.

In the foreign exchange market, the Brazilian real BRBY edged up 0.12 percent to 1.663 per U.S. dollar. The real gained for the third straight session, buoyed by expectations of a surge in capital flows into the country now that it has won an investment-grade credit rating from Standard & Poor's.

"The market is expecting inflows in the near term," said Gerson de Nobrega, a treasury manager at Banco Alfa de Investimento in Sao Paulo.

Still, trading was cautious as investors awaited more details on the sovereign wealth fund that Brazil's government is preparing to launch next month. Finance Minister Guido Mantega will hold a news conference later on Tuesday to offer more information on the fund, which will manage up to $20 billion.

"That could directly affect interest rates and the exchange rate," Nobrega said.