By Don Nico Forbes

Inflation in Germany, France and Italy cooled more than expected this month, suggesting price pressures are beginning to soften amid falling energy costs due to easing tensions between the U.S. and Iran.

In Germany, consumer price growth slowed to 2.4% on year from 2.7% in May, according to EU-harmonized data published by German statistics agency Destatis on Tuesday.

A consensus of economists polled by The Wall Street Journal had expected inflation at 2.5%.

Destatis said the rate of energy-price increases slowed again in June.

Separate data released Tuesday showed French inflation also slowing to 2.0% from 2.8%, while consumer price growth in Italy cooled to 3.0% from 3.2%. Both came in lower than economists' forecasts of 2.3% and 3.2%, respectively.

The easing in inflation follows a significant fall in energy prices over the month of June. Oil prices declined in anticipation of a tentative peace deal between the U.S. and Iran in mid-June, and have since fallen to their lowest levels since the conflict began, with markets increasing bets on a resumption of regular flows through the Strait of Hormuz.

"As the situation in the Middle East stabilizes, the inflation shock is also subsiding," Stephanie Schoenwald, economist at KfW Research, said in a note.

Cooler inflation comes as a welcome sign for the European Central Bank, which earlier in June raised interest rates for the first time in almost three years, becoming the first major central bank to take action to tackle rising prices driven by the war in Iran.

Questions remain over whether the central bank will opt to hike rates for a second time, but today's inflation data will weaken the case, Jack Allen-Reynolds, deputy chief eurozone economist at Capital Economics, said in a note.

"If oil and natural gas prices remain around their current levels, we think lower energy inflation will drag the headline rate down to about 2.5% in July, well below the ECB's forecast," he said.

Still, policymakers are likely to remain cautious as they assess whether recent energy-driven price pressures prove temporary or have longer-lasting price effects.

ECB President Christine Lagarde said Tuesday that the decision to hike interest rates was based on the bank's inflation projections, with its forecasts showing that inflation in the eurozone would remain above the 2% target through 2027 and 2028 without tighter policy.

In May, core inflation--which strips out volatile energy and food prices--jumped unexpectedly to 2.5%, highlighting the risks of higher oil prices spreading beyond energy markets.

Meanwhile, renewed tensions in the Middle East in recent days have raised concerns that disruption to shipping through the Strait of Hormuz could prove more prolonged than markets had anticipated after news of the interim peace agreement, keeping energy prices in the spotlight.

"Whether consumer price inflation will continue to decline in the coming months remains to be seen...The situation in the Persian Gulf remains fragile, and gas prices have not followed the rapid decline in oil prices," Schoenwald said.

On Monday, data showed that inflation in Spain remained stronger than anticipated in June, with electricity and gas maintaining upward pressure on prices.

Inflation figures for the eurozone as a whole will be published Wednesday.

Write to Don Nico Forbes at don.forbes@wsj.com