* Stocks choppy as investors await Europe progress
* Bovespa posts 2.34 bln reais net foreign outflow in May
* Brazil Bovespa nearly flat, Mexico IPC down 0.13 pct
By Asher Levine and Danielle Assalve
SAO PAULO, June 5 (Reuters) - Latin American stocks seesawed on Tuesday after talks between Group of Seven finance ministers failed to produce concrete measures to solve the worsening euro zone debt crisis.
The MSCI Latin American stock index rose for a second straight session, adding 0.19 percent to 3,328.50.
Shares gained early in the session, with bargain-hunters snapping up stocks of the most widely-traded companies as G7 finance ministers held an emergency teleconference to discuss a solution to the euro zone debt crisis.
However, those shares retreated after the meeting closed without an agreement on joint action.
Worries over a worsening debt crisis in Europe's 17-member currency bloc has led to a sell-off of riskier Latin American equities in favor of safe-haven assets such as the U.S. dollar.
"It's mostly market turnover. Today's gain doesn't translate into a change in the trend, because the buying needs to be consistent, and today we are not seeing enough money coming in to support the market," said Ariovaldo Santos, head of equities at brokerage H.Commcor in Sao Paulo.
"People are buying at the open, but depending on the market, are often exiting their positions on the same day."
Brazil's benchmark Bovespa stock index gained 0.17 percent to 53,507.76 after slipping in and out of negative territory earlier in the session.
Exchange operator BM&F Bovespa rose 1.88 percent, while preferred shares of state-controlled oil producer Petrobras anchored gains, losing 0.78 percent.
Many foreign investors exited the Bovespa in May, when the market posted a net outflow of 2.34 billion reais ($1.15 billion) in foreign funds, the biggest net outflow of the year.
"This scenario, where we have very little Brazilian money in the market, leaves the Bovespa more vulnerable to the flow of foreign funds," said Paulo Esteves, chief analyst with Gradual Investimentos in Sao Paulo.
"It's cowardly money, which at the first signs of a storm runs back to its owner and makes our market vulnerable, which explains why the Brazilian market can fall even more than markets at the center of the European crisis," he added.
Mexico's IPC index slid for a fifth straight day, losing 0.13 percent to 37,013.21, its lowest level in two weeks.
Telecommunications firm America Movil, controlled by billionaire Carlos Slim, lost 0.91 percent, contributing most to the index's losses, while lender Grupo Financiero Banorte rose 1 percent.
The IPC has been testing 37,000 points over the last two sessions, with the next key support at 36,800 points, said Juan Jose Resendiz, a technical analyst at bank Ve Por Mas in Mexico City. If the IPC breaks below that level and stays there, it could mean further movement southward toward 36,000, he added.
Chile's IPSA index capped a two-day loss, adding 0.03 percent to 4,207.47 as a technical indicator known as the relative strength index returned from "oversold" territory.
Retailer Cencosud rose 1.03 percent, driving gains in the index, while industrial conglomerate Copec lost 0.52 percent.
$1 = 2.0264 Brazilian reais Additional reporting by Rachel Uranga in Mexico City; Editing by Diane Craft