(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.

The downside surprise in the wholesale price data on Thursday sparked a partial reversal, with traders of futures tied to the Fed's policy rate now seeing about an equal chance of a July start to policy easing, versus September.

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.