(Reuters) - Market bets rose on Friday that the Federal Reserve will cut interest rates by September and do so again in December after a government report showed a key measure of U.S. inflation weakened last month.     Traders of futures contracts tied to the Fed policy rate now see about a 68% chance of a rate cut by the Fed's September meeting, up from about 64% earlier, after the data showed inflation by the personal consumption expenditures index did not rise at all from April to May.

(Reporting by Ann Saphir; Editing by Sharon Singleton)