Housing fuels and utilities cost 1.8 percent more in June than in May, and the cost of shelter increased 0.5 percent.
Prices also rose for the food (0.8 percent), tobacco (1.5 percent) and owners' equivalent rent (0.3 percent).
Excluding food and energy products, the so-called core index rose 0.3 percent last month, slightly more than economists had predicted. Core inflation is up 2.4 percent since June 2007.
The Fed has warned about higher inflation for months, although Bernanke has repeatedly said that the nation does not face the runaway price increases of the 1970s.
But this week's economic reports signal the difficult situation faced by policymakers. A measure of retail sales released Tuesday showed that consumer spending has nearly stagnated, a sign that economic growth is slowing. But the Fed cannot lower interest rates without risking more inflationary problems.
The bleak report adds to the financial woes of the past week, including the near-meltdown of the nation's biggest mortgage finance companies and continued turmoil in the stock markets.
In a separate report yesterday, the Fed said industrial production rose 0.5 percent in June after slipping 0.2 percent in May, exceeding economists' expectations. The increase, the biggest since a 0.6 percent gain in July of last year, reflected an end to an automotive production strike rather than any widespread strength in the economy.
The Associated Press contributed to this article.
