The July CPI report adds to the case for the Fed to hold rates steady next month, said Lindsay Rosner, head of multisector fixed-income investing at Goldman Sachs Asset Management.

"Contained core inflation adds to the encouraging signs in last month's release of a moderation in underlying inflation, helping strengthen the case for a September hold," Rosner said. "With another round of inflation data due before the September FOMC meeting, it remains all to play for, but today's in-line report was a good start."