Home-buying demand has surged in the past year due to low mortgage-interest rates, and existing-home sales are on track to hit their highest annual level since 2006. Fierce buyer competition for a limited number of homes for sale has pushed prices to record highs.

The Case-Shiller index, which measures repeat-sales data, reports on a two-month delay.

The median existing-home sale price in November rose 13.9% from a year earlier to $353,900, the National Association of Realtors said earlier this month.

Rising home prices are pushing some buyers out of the market. While the number of home sales rose in November, the proportion of first-time buyers fell to 26%, the lowest level since January 2014 and down from 32% a year earlier, according to NAR.

“U.S. home prices moved substantially higher, but at a decelerating rate,” said

Craig Lazzara,

managing director at S&P Dow Jones Indices. “That said, October’s 19.1% gain in the national composite is the fourth-highest reading in the 34 years covered by our data” with the top three being the three months preceding October.

The Case-Shiller 10-city index gained 17.1% over the year ended in October, compared with a 17.9% increase in September. The 20-city index rose 18.4%, after an annual gain of 19.1% in September. Price growth accelerated in six of the 20 cities.

Economists surveyed by The Wall Street Journal expected the 20-city index to gain 18.6%.

Phoenix had the fastest home-price growth in the country for the 29th straight month, at 32.3%, continuing its record streak in the top spot. Tampa posted the second-fastest growth, at 28.1%.

A separate measure of home-price growth by the Federal Housing Finance Agency also released Tuesday found a 17.4% increase in home prices in October from a year earlier.

Write to David Harrison at david.harrison@wsj.com and Nicole Friedman at nicole.friedman@wsj.com