Home prices increased at the fastest rate in seven years, jumping 10.9 percent in March, according to data released Tuesday, as buyers continued to compete for a limited supply of homes and the spring buying season kicked off.

Prices rose in all 20 cities tracked by the Standard & Poor’s Case-Shiller home price index. Phoenix, San Francisco and Las Vegas led the pack, with home prices rising more than 20 percent in each of those cities compared with a year ago.

Home prices in Washington rose 7.7 percent from a year ago, according to the closely watched index. They were up 1.7 percent from February.

Nationally, home prices in the first quarter were back to their 2003 levels but remained below their 2006 peak levels, according to the report.

The latest figures reflect a resurgent housing market — an important engine for the economy — that is still grappling with low inventory. “Without the housing recovery, the U.S. [would be] on the verge of a recession,” said Lawrence Yun, chief economist for the National Association of Realtors.

The housing market has shown few signs of slowing down, as low mortgages have driven buyers, including Wall Street investors, into the market and foreclosure levels have begun to decline. New-home sales in April increased 29 percent compared with a year ago, while sales of existing homes rose nearly 10 percent, according to data released last week.

But new-home construction, which could help alleviate pressure on prices, is far below desired levels, analysts say.

If prices continue to rise at their current pace without an increase in personal income, which would make homes more affordable, or a rise in interest rates, which would damp demand, it could raise concerns that the market is overheating, analysts said.

But it isn’t time to start worrying about another housing bubble, they said. Bank lending standards are tougher than pre-crisis levels and the recent price increases are still far from the frenzy seen during the early 2000s, they said.

“The thing that would worry me is if you were to see low-quality financing again,” said Craig Lazzara, senior director at S&P Dow Jones Indices. “Gains in prices are not being driven by a financing merry-go-round, but are real.”

As long as interest rates remain low, rents stay expensive and the job market improves, the housing market will continue to recover, Lazzara said.

Economists expect home prices to rise throughout 2013. That’s a mixed blessing, Yun said. The price increases help build wealth for homeowners and lift those who owe more than their homes are worth out of negative equity, but discourage new buyers, he said.

“The only people who are not smiling are the buyers,” he said.

The positive housing data helped lift stocks. The Dow Jones industrial average and the broader Standard & Poor’s 500-stock index both gained about 0.6 percent Tuesday. The Dow closed at a new high of 15,409.39.

The market was also helped by government data showing that consumer confidence climbed to its highest level in five years, driven by optimism about the economy. The data was released Tuesday.