A national measure of prices rose 5.4% from a year earlier, according to data from S&P CoreLogic Case-Shiller. That compares with a 5.9% annual increase in May.

While listings are ticking up, house hunters are still struggling to find affordable properties. But thanks to high mortgage rates, there aren't enough buyers in the market to create the level of competition that would drive prices up more significantly. Case-Shiller's index for June tracks a three-month period starting in April, a time when 30-year borrowing costs largely hovered around 7%.

The price data shows "above-trend real price performance when accounting for inflation," Brian Luke, head of commodities, real and digital assets at S&P Dow Jones Indices, said in a statement Tuesday. "Home prices and inflation continue to factor into the political agenda coming into the election season."

While both home-price gains and inflation have slowed, "the gap between the two is larger than historical norms, with the national index averaging 2.8% more than the consumer price index," Luke said. "That is a full percentage point above the 50-year average."

The Federal Reserve is expected to start cutting its benchmark interest rate next month, potentially putting some downward pressure on mortgage costs. But many economists expect it will take much deeper declines to nudge reluctant buyers and sellers off the fence.  

A measure of prices in 20 cities rose 6.5% from a year earlier, compared with a 6.9% annual gain in May. New York had the highest increase in June, followed by San Diego and Las Vegas with 8.7% and 8.5%, respectively.