The Fed’s favorite inflation gauge cooled in July.

The Federal Reserve’s preferred measure of inflation eased in July as gas prices fell following a sharp run-up earlier in the summer, a widely expected moderation that could nevertheless provide policymakers positive news as they battle the most rapid price gains in decades.

The Personal Consumption Expenditures index, which the Fed tries to keep climbing at a 2 percent annual rate on average over time, was up by 6.3 percent in July compared to a year earlier. While that is still far more inflation than the central bank wants, it is a slowdown from the 6.8 percent increase over the year through June.

And on a monthly basis, the price index declined by 0.1 percent, an even bigger pullback than economists had expected.

Because part of the decline was a result of falling gas prices, which are volatile and could jump again, officials may not take the cool-down in headline inflation alone as a major signal. But economists closely watch a so-called core inflation measure that strips out fuel and food prices to get a better sense of underlying price pressures, and that measure also offered some encouraging news.

Core inflation slowed to a 4.6 percent annual increase, compared with 4.8 percent in June. And on a monthly basis, the core index slowed to a 0.1 percent gain, a pullback from the prior month and less than the 0.2 percent economists in a Bloomberg survey had expected.

Fed officials are looking for decisive and sustained evidence before they deviate from their plans to restrain the economy to slow down lending and spending, and bring price increases under control. Friday’s report was likely an early — but not a conclusive — step in the right direction.

The central bank has sharply raised interest rates, which were near zero in March, to a range of 2.25 to 2.5 percent. Investors are keenly focused on the Fed’s Sept. 20-21 meeting, when, officials have signaled, they could lift interest rates by an unusually large three-quarters of a point — matching their last two moves — or a more modest but still meaningful half point.

While the Fed has signaled that slowing down rate increases in coming months could be appropriate, officials have not provided definite guidance about when that slowdown may begin or how high rates may ultimately go. Several policymakers have signaled that the central bank is likely to need to lift rates meaningfully higher to restrain the economy enough to bring price increases back under control.

“We have to get interest rates higher to slow down demand and bring inflation back to our target,” Esther George, president of the Federal Reserve Bank of Kansas City, said during a Bloomberg Television interview this week.

Ms. George, speaking from the central bank’s annual symposium near Jackson, Wyo., suggested that rates might need to climb above 4 percent and stay there for a while. That is slightly out of line with what investors expect: Market pricing suggests that the Fed will lift rates up to nearly 4 percent by next summer before beginning to reduce them again.

Central bankers have signaled that they are determined to bring inflation fully under control, rather than beginning to restrain the economy and then pulling back. That happened during the 1970s: The Fed did not successfully lower high inflation over the course of that decade as it reversed course on rate increases several times. Economists now blame that vacillation for how ingrained inflation became, and how much pain the central bank had to inflict in the 1980s to finally wrestle price increases under control.

Markets are hoping to get a clearer sense of how the Fed is thinking about inflation and rates at 10 a.m. Friday, when Jerome H. Powell, its chair, is slated to speak at the Jackson Hole conference. His speech is always one of the most closely watched events of the economy year, and has taken on heightened importance this year as painfully rapid inflation and the prospect of a policy-induced recession focus public attention on what the Fed may do next.