* Chilean peso, Peruvian sol rise as copper prices advance * Brazil 2022 budget signed by Bolsonaro * Oil rig fire to hit Mexican crude output (Adds details, updates prices) By Shreyashi Sanyal and Ambar Warrick Aug 23 (Reuters) - Most Latin American currencies came off session highs on Monday as uncertainty over U.S. monetary policy ahead of a major Federal Reserve event offset a sharp recovery in commodity prices from last week"s losses. Chile"s peso was among the few exceptions, rising 0.3% as the prices of copper, the country"s top export, advanced in anticipation that recovering global growth and the needs of a lower-carbon global economy will drive demand. World No. 2 copper producer Peru"s sol also rose 0.2%. A pullback in the dollar from nine-month highs provided emerging market currencies some breathing space after fears of earlier-than-expected policy tightening by the Fed, and rising COVID-19 cases saw them log their biggest weekly drop in two months. But most Latin American currencies were muted as investors now looked to more cues from the Fed during its Jackson Hole Economic Symposium, starting later this week. Global markets started the week on strong footing, with Asian stocks and currencies leading gains after a report from China"s health authority showed no new locally transmitted cases of COVID-19 for the first time since July. "The week starts with improved risk sentiment on the market after the stock markets in Asia were able to recover somewhat in the first few hours of trading and since the pandemic seems back under control in China," said Esther Reichelt, foreign exchange and emerging markets analyst at Commerzbank. Reichelt also pointed to investors being more cautious than optimistic; "concerns from last week are still having an effect ... even though it was certainly not a new realization last week that the Delta variant is increasingly spreading." Brazil"s real was largely flat after touching a more-than three-month low on Friday. Investors were watching for further developments in Brazil"s high debt levels, after President Jair Bolsonaro signed the 2022 budget law with a targeted deficit of 170.47 billion reais ($31.70 billion). While the deficit projection was lower than the massive $138 billion shortfall in 2020, it was still higher than 2019 levels. Mexico"s peso pared early gains as a fire at an offshore oil platform operated by state-run firm Pemex cut the company"s production by 444,000 barrels per day, and is likely to hurt one of Mexico"s top exports. MSCI"s index of Latin American stocks rose 0.9% after slumping 5.2% last week, its biggest weekly loss in nearly six months. Key Latin American stock indexes and currencies: Latest Daily % change MSCI Emerging Markets 1238.79 1.48 MSCI LatAm 2386.21 0.87 Brazil Bovespa 117698.97 -0.3 Mexico IPC 52152.83 1.44 Chile IPSA 4385.91 0.88 Argentina MerVal 68824.76 1.478 Colombia COLCAP 1336.71 0.74 Currencies Latest Daily % change Brazil real 5.3779 0.12 Mexico peso 20.3334 0.07 Chile peso 783.53 0.31 Colombia peso 3873.59 -0.09 Peru sol 4.0967 0.27 Argentina peso 97.4000 -0.08 (interbank) (Reporting by Shreyashi Sanyal and Ambar Warrick in Bengaluru; editing by Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.