Consumer inflation held steady at 2.1 percent yearly in June, the Bureau of Labor Statistics reported Tuesday morning, after rising the previous four months.

The good news for consumers worried about the cost of food is that food prices moderated in the month, with grocery prices flat. The bad news is that gasoline prices spiked 3.3 percent, driving two-thirds of the measured Consumer Price Index inflation.

For the Federal Reserve, which is trying to stabilize inflation at 2 percent, the report is a mixed bag. Headline inflation flattening out raises the possibility that the months-long move away from very low inflation may have been yet another short-term fluctuation and not a longer trend back toward normal.

Core inflation, a less-volatile measure of inflation that strips out changes in food and energy prices, slowed slightly to 1.9 percent.

Last week, the BLS reported that inflation had stopped rising in June for sellers. The Producer Price Index, which measures prices from the perspective of producers, slowed from 2 percent in May to 1.9 percent in June.

Inflation remains even lower in the Fed's preferred gauge, which is the Personal Consumption Expenditures Index maintained by the Bureau of Economic Analysis. The latest PCE data, for May, showed headline inflation at 1.8 percent, and core inflation at just 1.5 percent.

In other words, even with CPI inflation at 2.1 percent, there's still a long way to go as far as Federal Reserve Chairwoman Janet Yellen and the Fed are concerned. In their latest projections from June, Fed officials only see inflation budging up to around 1.7 percent by the end of the year.

That's only slightly below long-term expectations for inflation. Using a model based on implied rates from bond markets and forecasters' expectations, the Federal Reserve Bank of Cleveland puts 10-year expected inflation at 1.83 percent.