Seattle-area home prices gained again in June, but the rate of growth slowed in line with a national slowdown in price increases, according to the S&P/Case-Shiller 20-city index released Tuesday.

The average price of existing single-family homes sold in King, Snohomish and Pierce counties was up 1.1 percent over May, when the average price rose 1.4 percent. The June home prices represent an 8.6 percent annual gain.

Nationally, home prices in June gained 0.9 percent over the month and 6.2 percent over the year, while the 20-city index gained 1 percent over the month and 8.1 over the year. That is down from 9.4 the month before and the smallest annual gain since December 2012.

For the first time since 2008, all of the cities in the 20-city index saw their annual growth rates slow from the previous month, index officials said.

“Home-price gains continue to ease as they have since last fall,” said David Blitzer, who oversees the index. “While all 20 cities saw higher home prices over the last 12 months, all experienced slower gains,”

The 20-city index is back to its fall 2004 levels but still about 17 percent short of its summer 2006 peak. The Seattle market is still about 11.6 percent below its summer 2007 peak, according to the index. Sunbelt cities — Las Vegas, Phoenix, Miami and Tampa — all remain a third or more below their peak prices, while Detroit remains the only city below its January 2000 levels.

Stan Humphries, chief economist of Seattle-based Zillow, said local dynamics determine individual market performances, so consumers should not assume national numbers apply evenly to their local market.

“Different markets boast sometimes dramatically different fundamentals, including differences in the balance between buyers and sellers, varying levels of inventory, faster or slower paces of appreciation and wider or narrower gaps between asking prices and selling prices,” he said in a statement.

The average rate for a 30-year mortgage fell to 4.1 percent this week, the lowest level this year, according to Freddie Mac. Many economists project that the Federal Reserve will begin to raise short-term interest rates in 2015 because the economy has strengthened, which could cause mortgage rates to rise from relative lows and make it more expensive to borrow.

“Rising mortgage rates won’t send housing into a tailspin, but will further dampen price gains,” Blitzer said.

Coral Garnick: 206-464-2422 or cgarnick@seattletimes.com. On Twitter @coralgarnick