Brazil's Bovespa was one of the world's worst-performing indexes last year as Latin America's largest economy suffered from slow growth and high inflation. Mexican stocks were supported by optimism about an economic reform drive.
Latin American stocks may suffer again this year on bets that a tapering of US monetary stimulus will sap demand for higher-risk assets, such as emerging market equities, and concerns that slower growth in China will hurt local exporters.
But many of the region's stocks suffered more than other global peers last year, which was tough on emerging markets. That could make them attractive destinations for money mangers with fresh cash at the start of 2014 and help fuel a rebound.
Brazil's Bovespa ticked down 0.01 percent to 50,973.62 points as a new index weighting took effect. Data on Monday showed growth in China's services sector slowed sharply in December to its lowest point since August 2011.
Brazilian data also was negative. HSBC's Composite Output Index for Brazil, which includes manufacturing activity, dipped in December.
Shares of state-run oil firm Petrobras rose 1.22 percent as they rebounded off a more than four-month low, while iron ore miner Vale SA bounced back from its lowest level since late November. The recoveries may be short lived, however, as analysts said commodities producers may be vulnerable to worries over Chinese demand.
Financial exchange operator BM&FBovespa SA lost 2.53 percent.
Mexico's IPC index fell 1.28 percent to close at 41,525.95 points, as shares in copper miner Grupo Mexico slid 2.9 percent.