(Reuters) - The Federal Reserve could start interest-rate cuts as early as its late-July meeting, traders bet on Thursday, after a government report showed producer prices in March rose a bit less than expected.    On Wednesday a higher-than-expected reading on March consumer prices -- the third upside surprise in a row on the monthly inflation readings -- prompted traders to push out expectations for a first Fed rate cut to September, from an prior view that cuts would start in June.

New York Federal Reserve Bank President John Williams, in remarks prepared before Thursday's data was released, said he expects further progress on inflation, though with bumps along the way.

(Reporting by Ann Saphir; Editing by Sharon Singleton and Chizu Nomiyama)