• Key insight: Headline CPI inflation was 3.5% in June, slower than the 4.2% growth tracked in May. Core inflation also ticked down from 2.9% to 2.6%.
• Expert quote: "I would be very pleased to see a lower reading on core inflation, but after its escalation over the first half of this year, I will need to see several months of lower readings to feel that inflation is moving in the right direction." — Federal Reserve Gov. Christopher Waller
• Forward Look: The Federal Open Market Committee will weigh this inflation report against weaker job growth and other economic indicators during its monetary policy meeting later this month.

Inflation slowed down in June, taking the pressure off the Federal Reserve to increase its benchmark interest rate later this month.

Overall prices in June were up  3.5% from a year ago, according to the Bureau of Labor Statistics's consumer price index, released Tuesday morning. While still well above the Fed's 2% target, the rate of increase was noticeably slower than May, when headline CPI inflation rose 4.2%.

The Fed's preferred inflation index, the personal consumption index from the Bureau of Economic Analysis, rose 4.1% in May. The two indexes differ slightly in composition but move in the same direction.

Core inflation, which factors out volatile factors like food and energy, rose 2.6% on an annualized basis last month, an improvement against May's 2.9% growth rate. This was the first time since January that a core inflation reading came in lower than the previous month. 

The June reading is positive for the economy in both the near and long term. The energy portion of the index declined 5.7% last month, indicating that the since-lapsed ceasefire between the U.S. and Iran allowed gas and fuel prices to fall quickly. The slower growth in core prices indicates that underlying price expectations are not becoming unanchored.

For policymakers, the reading reduces the urgency to increase interest rates in the immediate future. In a Monday afternoon speech, Fed Gov. Christopher Waller said he would be closely tracking the core portions of Tuesday's CPI report as well as Wednesday's producer price index for signals about where prices are heading.

"The question is, will core inflation continue on its upward trajectory, or has it reached a turning point where it will begin to decline back toward our 2% target?" Waller mused on Monday. "The direction it takes has very different implications for the path of monetary policy."

Waller said he is concerned that a surge of investment into artificial-intelligence capabilities and companies could be driving sustained price growth, one that would outlive any conflict-induced oil shocks. He noted that core inflation began trending up before the outbreak of war in the Middle East.

Tuesday's report is a step in the right direction, if the Fed is to avoid a rate cut this year, but Waller said it alone will not be enough to dismiss the idea of a shift toward tighter monetary policy.

"I would be very pleased to see a lower reading on core inflation, but after its escalation over the first half of this year, I will need to see several months of lower readings to feel that inflation is moving in the right direction," he said, adding that he would expect it to be appropriate to "continue to hold the policy rate at its current target range."

Fed Chair Kevin Warsh will also be asked to weigh in on Tuesday's inflation reading during a hearing in front of the House Committee on Financial Services.

Warsh has said he is committed to returning the Fed to its 2% inflation target, but has also suggested that the central bank should rethink the way it approaches inflation and its handling of monetary policy more broadly.