* Argentine stocks at over 3-month low * Brazil"s real flat after c.bank holds rates, stocks rise * Mexican stocks fall in catch-up trade (Adds details, updates prices) By Susan Mathew and Ambar Warrick Sept 17 (Reuters) - Latin American currencies fell on Thursday after U.S. weekly jobless claims data pointed to a sluggish economic recovery, while Argentine assets plummeted in the wake of fresh capital controls. Argentine stocks sank 4% to their lowest since early June, while the peso continued to descend into record-low territory after the government earlier this week restricted dollar access to protect its scant forex reserves. The move brewed uncertainty over the country"s economic prospects, even as inflation appeared to be stabilizing. Brazil"s real was flat after the central bank held rates steady on Wednesday, as expected, after nine consecutive cuts. The bank pledged to stimulate the coronavirus-hit economy with "forward guidance" rather than more rate cuts. It warned that inflation in the short-term may be higher than previously thought. "The major evolution in this policy statement is the introduction of forward guidance," Sacha Tihanyi, deputy head of emerging markets strategy at TD Securities, said about Brazil"s central bank communique. "We believe this guidance should flatten the rates curve... In addition, we change our rate view to one in which the central bank remains on hold until fourth quarter of 2021, and then begins slow policy normalization." Brazilian stocks were a touch higher, outpacing their regional peers as oil and gas heavyweight Petrobras flagged strong investor demand for a bond buy-back and made progress in an expansion at its Rio de Janeiro liquefied natural gas (LNG) import terminal. The Mexican peso rose slightly, while the Colombian peso fell 0.7%. Chile"s peso broke a four-session losing streak as prices of copper, the biggest source of Chile"s export revenue, retreated. High-yield currencies in the emerging market space have drawn renewed interest in recent months, with economic readings slowly moving toward pre-pandemic levels. But sentiment still remains fragile, particularly in Latam, which is the worst-stricken region in the world by the virus. The World Health Organization"s Latam director said the region started to resume normal social and public life too early. Stocks in the region slumped, tracking moves on Wall Street after the U.S. Labor Department"s report showed the number of Americans filing new jobless claims remained at extremely high levels. Mexican shares slipped 1.4% in catch-up trade after a holiday on Wednesday, while Colombian stocks shed 0.4%. The Peruvian sol was largely flat, ahead of President Martin Vizcarra facing an impeachment hearing on Friday after the country"s constitutional court rejected his appeal to delay congressional efforts to remove him from his post. Key Latin American stock indexes and currencies: Stock indexes Latest Daily % change MSCI Emerging Markets 1106.09 -0.98 MSCI LatAm 2006.95 -0.03 Brazil Bovespa 99964.43 0.29 Mexico IPC 36218.87 -1.39 Chile IPSA 3729.64 0.35 Argentina MerVal 40342.30 -4.329 Colombia COLCAP 1190.87 -0.42 Currencies Latest Daily % change Brazil real 5.2459 -0.13 Mexico peso 20.8956 0.16 Chile peso 762.6 -0.31 Colombia peso 3713.8 -0.74 Peru sol 3.5218 0.11 Argentina peso 75.3100 -0.08 (interbank) (Reporting by Susan Mathew in Bengaluru; Editing by Dan