Prices continued to rise in the US last month, despite a sharp increase in interest rates to stamp out inflation.

The rate of inflation was 3.2% over the year to July, driven by higher housing, car insurance and food costs, the Labor Department said.

That was up from 3% in June, which was the lowest rate in more than two years.

Analysts had expected the increase in the headline rate, after relatively weak price inflation last July.

But that said the report from the US Labor Department offered other signs that price increases were subsiding.

“Underlying inflation is heading in the right direction,” said Hussain Mehdi, macro and investment strategist for HSBC Asset Management, while Harvard economist Jason Furman called the latest figures “unambiguously good news”.

The US central bank has raised its benchmark interest rate to more than 5.25% – the highest level in 22 years – in a bid to cool the economy and ease the pressures pushing up prices.

Inflation in the US hit a peak of 9.1% last year, far above the US Federal Reserve’s 2% target.

However, it has eased significantly as the shock to food and energy prices from the war in Ukraine has faded.

Ryan Sweet, chief US economist at Oxford Economics, said the decline did not imply that it was “mission accomplished” for the rate-setting central bank.

“Still, we expect the Fed to skip rate hikes in September and November, when inflation should have decelerated even further,” he said.

Compared with June, core prices rose at a relatively modest 0.2%. That was the same pace as between May and June.

Prices for some items, including used cars and airline fares, dropped last month.

Many analysts are expecting costs for housing, which is weighted heavily in US inflation calculations, to start to ease in coming months, pointing to independent reports showing a slowdown in the growth in rental rates.

But a recent rise in fuel prices could mean it takes longer than hoped for inflation to ease its grip on the economy.

Though the prices remain lower than a year ago, the average national price for regular gasoline in the US jumped above $3.80 per gallon earlier in August, up from about $3.50 a month earlier, according to the motor club association AAA.

“The recent trend is encouraging and confirms that inflation is headed in the direction [the Fed] wants,” said Wells Fargo economist Sarah House. “That said, we are cautious about getting overly excited.”