TAMPA - Tampa Bay's housing market continued to bloom last month amid the best spring selling season in years, but tight supplies of homes for sale are squeezing hopeful buyers out of deals, new Realtors data show.

Nearly 3,200 local homes sold last month, making it Tampa Bay's busiest sales month in seven years, multiple listing service data show. And the typical buyer signed a contract within a month, the fastest pace of deal-making since the boom.

With so much demand, the supply of homes for sale has failed to keep up, sparking bidding wars and rapid-fire sales.

The number of months it would take the market to sell out with no new homes for sale plunged to four months in Pinellas and three months in Hillsborough, far below what Realtors said is a healthy six-month supply.

"I don't think the average homeowner really understands how low our inventory is, and how great the demand is," Re/Max Bay to Bay agent Rae Catanese said. "It is extremely frustrating for buyers. It's too low, it's unhealthy, and I don't know if that's going to change any time soon."

Rising prices have helped once-underwater home­owners resurface with equity and convinced reluctant buyers to return to the market.

Florida has seen 16 straight months of year-over-year price gains, and home sales statewide jumped 17 percent over last year, the Florida Realtors said Wednesday.

Home sales across the country also sped up last month to their quickest pace since November 2009, when the market spiked due to the $8,000 first-time homebuyer tax credit, the National Association of Realtors said. American home prices have increased year-over-year for 14 months in a row.

As prices climb, more and more home sellers are joining the market out of choice, not distress.

Cheap credit has also helped entice buyers to the market, with the average interest rate for a 30-year fixed mortgage falling to 3.45 percent, mortgage giant Freddie Mac said. That's down from 3.91 percent in April 2012.

"The robust housing market recovery is occurring in spite of tight access to credit and limited inventory," Realtors chief economist Lawrence Yun said in a statement. The only way to "tame price growth to a manageable, healthy pace" unhindered by scant supplies, he added, would be quicker construction of new homes.

In Tampa Bay, builders broke ground on nearly 1,500 homes in the first three months of the year, 46 percent more than the same time last year, construction research firm Metrostudy said. By the end of March, 3,600 homes were under construction or finished and awaiting buyers.

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