Sales of previously owned homes continued rising in June, helped by a slight pullback in mortgage rates and the continuing confidence of gainfully employed Americans. Indeed, July saw a rebound in consumer confidence, driven by Americans' optimism that jobs will continue to be plentiful.

Existing home sales

, which account for the bulk of U.S. housing market activity, rose 2.8% in June to a 5.23 million annual rate, following a 4.3% rise in May, the

National Association of Realtors

said Tuesday.

The

consumer confidence index

, a measure of the average American's comfort with the current economic situation, rose 2.5 points to 141.7 in July after June's 5.5 point decline, the

Conference Board

, a private research group, reported Tuesday. The data are based on a representative sample of 5,000 U.S. households and measured relative a reading of 100 in 1985.

Both pieces of data suggest that some key areas of the U.S. economy might be on the rebound after slumping in the second quarter.

Housing markets and home building had been on the decline for several months, and policy makers and economists cautiously believed that higher mortgage rates were curbing American's home-buying enthusiasm. But the June rebound might suggest otherwise.

Similarly, June's sharp decline in consumer confidence had been seen as a sign that consumers, who account for roughly two-thirds of the nation's economic output, might have been hunkering down in the face of higher financing rates. But the rebound in confidence might point to renewed consumer spending activity.

"Consumer confidence readings continue to indicate a strong overall economy," said Lynn Franco, director of consumer research at the Conference Board. "Consumers are not only optimistic about current conditions, but their expectations for the next six months signal continued low unemployment and minimal inflationary pressures."

In testimony on monetary policy last week,

Federal Reserve

chairman Alan Greenspan said some indications were emerging that portions of the economy were slowing down. These signs, he said, include higher household debt, the near-saturation of consumers' appetite for long-lasting durable goods like automobiles and appliances, and stagnating stock prices.

But Greenspan also warned that growth might accelerate again, leading to renewed efforts by the central bank to raise interest rates to slow economic growth to a sustainable level. Greenspan also warned that the recent strength in consumer confidence and home sales activity could be a sign that the economy might be heating again.

Some economist held a similar view. "As long as consumer confidence stays high, which we believe it will provided that the labor markets stay strong and the stock market does not collapse, consumption growth is likely to reaccelerate in the coming months," said Joseph LaVorgna, senior economist at

Deutsche Bank

.

The Fed has raised short-term interest rates six times in the past year in an attempt make it more costly for consumers and businesses to borrow and spend. By slowing spending, the Fed hoped to put supply and demand back into balance, reducing the risk of inflation that occurs when too many dollars chase a steady amount of goods. At its most recent meeting in June, the Fed's policymaking committee decided to keep interest rates steady, citing several slowing areas of the economy.