CORRECTED - Brazil stocks waver as Wall St slips, but currency up

(Corrects headline and paragraph 6 to reflect market's fluctuations, not decline)

SAO PAULO, June 23 (Reuters) - Brazil's stocks seesawed on Tuesday as oil giant Petrobras shares' gains were offset by worries about the health of the world economy.

U.S. existing home sales increased at a slower-than-expected pace in May, indicating the U.S. economy's recovery from a severe recession is likely to be tepid. Brazil's markets care about U.S. data as far as it's indicative of how the world's largst economy is doing.

Brazil's local currency gained slightly after the previous day's plunge.

Over the past three months, Brazilian assets have rallied as hopes for a global economic recovery whetted investors' appetite for risk and emerging market assets. But investors were now reassessing the extent of the economic rebound because of mixed data and an uncertain outlook.

Brazil's Bovespa index .BVSP was little changed, up just 0.01 percent, at 49,498.28 points in choppy trade after falling more than 3 percent in the previous session. The index is in negative territory in June after rallying for three straight months, but it has gained more than 31 percent so far in 2009.

The market's fluctuations occurred against the backdrop of losses on Wall Street, where U.S. stocks slipped as Boeing again delayed the first test flight of its Dreamliner aircraft and the existing home sales data raised concerns about the strength of a potential economic recovery.

Brazil's real gained 0.6 percent to 2.01 per U.S. dollar, but is still weaker for the month against the dollar.

"It's an adjustment after a very strong movement generated by a rise in risk-aversion abroad yesterday," said Silvio Campos Neto, chief economist at Banco Schahin.

The real has strengthened around 16 percent against the dollar so far this year -- a rally that has made government officials worried about the prospects for local exports.

At the stock exchange, financial shares led losses. Itau Unibanco (ITUB4.SA) shed 1.22 percent to 30.01 reais, Banco Bradesco (BBDC4.SA) fell 1.37 percent to 28.01 reais. Brazilian financial and commodities exchange operator BM&F Bovespa (BVMF3.SA) fell 1.01 percent to 10.80 reais.

Market heavyweight Vale (VALE5.SA) also weighed on the index, falling 0.43 percent to 29.81 reais even as copper prices rose.

The downside was limited by Petrobras (PETR4.SA), which gained 0.32 percent to 30.96 reais, rebounding after its 3.4 percent slump on Monday.

Steelmaker CSN (CSNA3.SA) also gained 0.7 percent to 41.95 reais after the company said it had hired 1,200 workers at its Volta Redonda plant following signs the market is recovering. Late last year, it had cut 1,300 jobs as the global economic crisis cut into demand for steel. Elsewhere in the sector, Gerdau (GGBR4.SA) gained 1 percent to 19.24 reais as metal prices rose.

Interest-rate futures <0#DIJ:> were broadly lower, with the central bank still widely expected to ease monetary policy further even if at a slower pace.

Last week Brazil's central bank said it saw "residual leeway" for future interest-rate cuts in minutes from its rate-setting meeting earlier in the month, signaling it will reduce borrowing costs at a slower pace. (Reporting by Ana Nicolaci da Costa and Vanessa Stelzer; Editing by Jan Paschal )