U.S. home rental prices rose at a steady rate in January, but prices barely budged or even dipped in parts of the Midwest and Mid-Atlantic.

Real estate data firm Zillow said Friday that prices increased a seasonally-adjusted 3.3 percent in January compared with 12 months earlier. But some major cities are finding themselves with an excessive supply of apartments and houses, reducing price pressures for renters.

In the wake of the Great Recession, more Americans are shifting away from home ownership, often because their low-incomes make it difficult to save for a down payment or they live in cities with expensive housing. The homeownership rate slipped to 64 percent at the end of 2014, the lowest level in two decades, according to the Census Bureau. Some of that decline also reflects the ravages from the housing bust that triggered the recession in late 2007, as foreclosures and overbuilding left plenty of empty houses.

Still, builders have started to respond to the greater demand as the job market improves and more millennials seek apartments. Over the past 12 months, there has been a 24.5 percent increase in groundbreakings for apartment complexes, according to a separate Census report released Wednesday.

As more supply comes onto the market, price pressures should ease for renters, said Svenja Gudell, director of economic research at Zillow. Modest increases or slight declines should help improve affordability, making it easier for renters to eventually transition to home ownership.

The additional supply is already evident in a few key markets.

Zillow reported that rents have fallen 0.5 percent in the Chicago area and 0.3 percent in Minneapolis over the past year.

"Chicago did a whole lot of overbuilding during the housing boom," said Gudell, noting that some select downtown neighborhoods in the Windy City still have prices rising at or above the national average.

Similarly, new apartment construction has been coming online around Baltimore and Washington, DC, where rental prices rose 1.5 percent and 1.3 percent, respectively. A separate report by the rental marketplace Apartment List found that rents for a two-bedroom apartment in metro Washington were averaging $1,990 a month, up just 0.1 percent over the past year.

Other parts of the country are experiencing a rental boom.

Rents surged 16.2 percent in Fort Myers, Florida, while the San Francisco Bay area also posted a double-digit gain.