MEXICO CITY, Aug 6 (Reuters) - Mexico's peso firmed to an 11-week high on Thursday as a drop in the number of new U.S. claims for jobless benefits spurred optimism about the pace of an economic recovery in the United States. The U.S. downturn has undermined demand for Mexican exports, driving the country into what could be its deepest recession since the 1930s. Signs of a U.S. recovery bode well for the battered peso currency and stocks. The peso firmed 0.37 percent to 12.9875 per U.S. dollar, easing back from early session highs of 12.93, its strongest since May 20. The U.S. data showing initial claims for state unemployment insurance fell added to optimism after the European Central Bank said it sees a gradual recovery in 2010. The peso's gains built on the previous day's surge triggered by credit rating agency Moody's decision to keep Mexico's debt rating outlook at stable. [ID:nN05513427] "Today's gains are follow-through from Moody's, helped by the U.S. data. We are seeing a a lot of corporate demand because people didn't think the peso could break 13," said a trader in Mexico City. "If the U.S. data keeps coming out strong, the peso could hold onto these levels, if not, it is heading back to 13.10 or 13.20," he said. The IPC stock index .MXX slipped 0.09 percent to 28,056. It had opened at its highest level since July. Top retailer Wal-Mart de Mexico (WALMEXV.MX: Quote, Profile, Research, Stock Buzz) gained 1.39 percent to 47.30 after posting better-than-expected sales figures for July after market close on Wednesday. [ID:nN05273539] Offsetting those gains, shares in wireless operator America Movil (AMXL.MX: Quote, Profile, Research, Stock Buzz) lost 0.87 percent to 29.50 pesos, tracking losses in telecommunications stocks on Wall Street. (Reporting by Michael O'Boyle; Editing by Kenneth Barry)

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