* U.S. new unemployment claims fall more than expected
* Leadership change underway in key trade partner China
* Brazil Bovespa up 0.45 pct, Mexico IPC flat
By Asher Levine and Danielle Assalve
SAO PAULO, Nov 8 (Reuters) - Latin American stocks rose on Thursday after Greece's government approved austerity measures crucial to unlocking an aid package and data showed an improvement in the U.S. labor market.
The MSCI Latin American stock index rose for a second session, adding 0.24 percent to 3,665.58.
Steelmakers and banks helped support Brazil's benchmark Bovespa index, while bottling group Femsa drove gains in Mexico's bourse.
The number of Americans filing new claims for unemployment benefits fell more than expected last week, U.S. Labor Department data showed on Thursday, fueling investor confidence over a recovery in the world's No. 1 economy.
Some concerns over the euro zone debt crisis were also relieved after Greece's parliament approved a controversial austerity package on Thursday needed to unlock international aid and avert bankruptcy.
"Positive labor market data in the United States helped boost the market and the Greek austerity package was a positive signal," said Gabriel Ribeiro, an analyst with Um Investimentos in Sao Paulo, adding that investors would continue to watch the Greece situation as the details get ironed out.
Investor attention also turned to China, where the government has begun a once-in-a-decade leadership change that could yield eventual shifts in economic policy.
China is Brazil's biggest trading partner and a key purchaser of Latin American commodities exports such as iron-one, soy, copper and petroleum.
"The key issue is whether the next leadership will pursue reforms to rebalance the economy towards consumption and away from investment," said Neil Shearing, Chief Emerging Markets Economist with Capital Economics in London. "Investment is very commodity-intensive and that's what really spurred Brazilian exports to China."
Brazil's benchmark Bovespa stock index recovered from early losses, rising 0.45 percent to 58,778.63 after finding support at its 75-day simple moving average.
"If the Bovespa loses steam and crosses below 58,400 it will head for 56,800," warned Fabio Cardoso, a partner at Adinvest in Rio de Janeiro. "In the short term there are no big drivers and little inflow so there's no real reason for big gains."
Steelmaker Usiminas gained 2.9 percent, contributing most to the index's gains, while Itaú Unibanco , Brazil's largest non-government bank, added 0.72 percent.
Grupo Cosan SA, Brazil's largest sugar and ethanol producer, gained 3.1 percent after posting a jump in quarterly income from the same period last year.
Shares of state-controlled lender Banco do Brasil SA slipped 1.5 percent after the nation's largest bank said Thursday that third quarter profit sank as provisions for bad loans rose and interest income fell.
Mexico's IPC index hovered near unchanged territory, with a 1 percent gain by bottling group Femsa helping offset a 0.9 percent loss by telecommunications firm America Movil.
Chile's IPSA index lost 0.12 percent to 4,251.36, as conglomerate AntarChile slipped 1.3 percent.
Latin America's key stock indexes at 1445 GMT: Stock indexes daily % YTD %
Latest change change MSCI LatAm 3,665.58 0.24 1.51
Brazil Bovespa 58,778.63 0.45 3.57
Mexico IPC 41,042.08 0.08 10.69
Chile IPSA 4,251.36 -0.12 1.77
Chile IGPA 20,857.63 -0.09 3.62
Argentina MerVal 2,377.12 0.29 -3.47
Colombia IGBC 13,938.93 -0.22 10.05
Peru IGRA 20,917.30 0.15 7.42
Venezuela IBC 363,575.72 0 210.65
(Editing by Bernadette Baum)