The core CPI—which excludes food and energy costs—climbed 0.16 percent from April to May.

"Fed officials will view today's report as showing some cooling in consumer spending, which points to less inflationary pressure. Our view of the U.S. economy is not as optimistic."

"It does open the door to a potential rate cut later in the year. It will take a few more readings indicating that inflation is coming down for the Fed to act."

Demand for workers is moderating, but the data likely doesn't amount to "an unexpected weakening" that would warrant a policy response.

The value of retail purchases increased 0.7% from February. Excluding cars and gasoline, sales jumped 1% month over month.

After the metric rose 3.8% rise year-over-year: "The sound you heard there was the door slamming on a June rate cut."

Even so, Fed officials are looking for more evidence that inflation is sustainably on a downward trend, and in the meantime, they're not rushing to cut interest rates.

At the end of last year, GDP rose at a 3.4 percent annualized pace, while GDI jumped 4.8 percent, the most in two years.