Home prices continued to rise throughout much of the country in September — fresh evidence of a housing market recovery, according to a closely watched report released Tuesday.

Home prices in 20 cities tracked by the Standard & Poor’s/Case-Shiller home price index rose 0.3 percent on a non-seasonally adjusted basis in September, compared with August. It was the sixth consecutive monthly increase.

Prices were up 3 percent, compared with the corresponding period in 2011.

“It is safe to say that we are now in the midst of a recovery in the housing market,” David M. Blitzer, chairman of the Index Committee at S&P Dow Jones Indices, said in a statement.

The Phoenix region, one of the hardest hit by the collapse of the housing sector, reported the biggest yearly gain. Home prices in that area rose 20.4 percent in September, compared with the corresponding period last year.

Home prices show continued improvement. (The Washington Post/Source: S&P/Case Shiller)

In the Washington area, home prices were up 3.2 percent, compared with that period in 2011.

But the housing market is headed into a traditionally slow period, and foreclosures are likely to comprise a larger portion of the market throughout the rest of the year, weighing on sale prices, said Stan Humphries, chief economist at Zillow, an online real estate company.

“September will likely be the last hurrah” for the index, Humphries said. “We expect the monthly numbers to be negative for the balance of the year.”

The housing market has been bolstered by low mortgage rates but remains far from a full recovery. Many people are still at risk of foreclosure, and home prices remain 29 percent below their 2006 peak levels.

That has left millions of homeowners who are “underwater” — owing more on their mortgages than their homes are worth — with negative equity that puts them at a higher risk of foreclosure.

“For negative equity to be erased entirely, we’ll have to get home values back to roughly peak level in nominal terms. That’s a multiyear affair, more than a decade, I would think,” Humphries said.