WASHINGTON — The Federal Reserve’s preferred inflation gauge ticked higher last month in a sign that President Donald Trump’s broad-based tariffs are starting to lift prices for many goods.

Prices rose 2.6% in June compared with a year ago, the Commerce Department said Thursday, up from an annual pace of 2.4% in May. Excluding the volatile food and energy categories, prices rose 2.8% in the past year, the same as the previous month, which was revised higher. The figures are above the Fed’s 2% goal.

The uptick in prices helps explain the central bank’s reluctance to cut its key interest rate this week, despite repeated demands from Trump that it do so. On Wednesday, the Fed left its key rate unchanged at 4.3%, and Chair Fed Powell suggested it could take months for the central bank to determine whether the import duties will cause just a one-time rise in prices or a more persistent increase in inflation.

On a monthly basis, prices ticked up 0.3% from May to June, while core prices also rose 0.3%. Both figures are higher than consistent with the 2% target.

The government’s measure of gas prices jumped 0.9% from May to June, while grocery costs rose 0.3%. Many longer-lasting goods that are heavily imported saw clear price increases, with furniture prices up 1.3% just last month, appliances up 1.9%, and computers up 1.4%.

The cost of some services fell dramatically last month, offsetting the price pressures from goods. Air fares dropped 0.7% from May to June, while the cost of hotel rooms plunged 3.6% just in one month.

Thursday’s report also showed that consumer spending rose 0.3% from May to June, a modest rise that suggests Americans are still spending cautiously. Adjusted for inflation, the increase was just 0.1%, the government said.

Consumers have been cautious all year. On Wednesday, the government said the economy expanded at a 3% annual rate in the second quarter, a solid showing but one that masked some red flags. Consumer spending, for example, rose at a lackluster 1.4% pace, after an even smaller gain of 0.5% in the first three months of the year. A sharp drop in imports in the April-June quarter, which followed a surge in the first quarter, provided a big lift to the government’s calculation of U.S. gross domestic product.

Earlier this month, the government reported that its more closely-watched consumer price index, its primary inflation measure, also ticked higher in June as the cost of heavily-imported items such as appliances, furniture, and toys increased.