WASHINGTON – Sales of previously occupied U.S. homes ticked up last month to the highest level in three and a half years, helped by a jump in the number of houses for sale.

The National Association of Realtors said Wednesday that sales rose to a seasonally adjusted annual rate of 4.97 million, up from 4.94 million in March.

Home sales have risen 9.7 percent in the past 12 months, evidence that the housing market is still improving. But sales have been roughly flat since November. The supply of available homes remains tight and many potential buyers aren’t able to get loans.

The number of homes for sale rose 12 percent in April from March to 2.16 million. But inventory is still almost 14 percent lower than a year earlier.

The increase in inventories partly reflects the beginning of the spring selling season. The supply of homes would be exhausted in 5.2 months at the current sales pace. That’s below the typical level of about six months.

More Americans are interested in purchasing homes: buyer traffic has risen 31 percent in the past year, the Realtors’ group said.

Rising demand and tight supply has pushed up prices. The median price of a home for sale jumped 11 percent last month from April 2012 to $192,800. That’s the highest in nearly five years.

The increase in prices partly reflects more sales of higher-priced homes. Sales of lower-priced homes are rising more slowly.

And sales of cheap foreclosed properties are falling. The proportion of distressed sales has fallen sharply in the past year, to 18 percent from 28 percent in April 2012. Distressed sales include foreclosed homes and homes in which the size of the mortgage exceeds the home’s value.