Oahu home prices stayed near record highs in March as buyers made about 20 percent more purchases and further cut into inventory that was already in tight supply, a new report shows.

The Honolulu Board of Realtors report released for publication on Wednesday said the median price for single-family homes sold last month was $725,000. That was up 4 percent from $700,000 in the same month last year and was third highest for any month. The record was $733,500 in January following the prior high of $730,000 in September.

For condominiums, the median sale price in March was $385,000. That was up 1 percent from the $380,000 median a year earlier and just shy of the $386,250 record set in December.

The high prices, industry experts say, are a result of a relatively small supply, which has been kept from growing much because of constraints on building more homes, and strong demand driven by job growth and low interest rates.

Jason Nishikawa, senior vice president at local brokerage firm Marcus & Associates, told a group of Honolulu Board of Realtors members last week that it’s tough to be an agent representing buyers in this market where they can face five or 10 competing offers.

“We’ve got a problem,” he said.

The solution, however, isn’t a quick or simple fix given that Hawaii faces a limited land supply, a tough and lengthy regulatory process for obtaining development permits and high costs for construction and land.

“Our housing situation on Oahu has now surpassed crisis mode,” he said, adding that he predicts the trend of rising prices, which make homes less affordable, will get worse.

Kalama Kim, president of the trade association for Oahu real estate agents, said housing inventory is shrinking fast. There were 844 single-family homes on the market at the end of March. That was down from 1,118 in February and was the first time in three years that inventory dropped below 1,000. The all-time low was 784 in April 2004.

“It appears housing inventory for single-family homes is approaching critical levels,” Kim said in a statement. “There’s been no letup in demand for housing on Oahu.”

There were 297 single-family home sales last month, up 22 percent from 244 sales a year earlier. Condo sales also surged 22 percent, to 491 last month from 403 a year earlier.

If the current pace of sales continues and no new inventory is added to the market, the existing inventory of single-family homes would be exhausted in 2.1 months and the inventory of condos would be exhausted in 2.3 months, the report said.

This measure known as months of remaining inventory had been running between 2.6 and 3.7 over the last two years. The last time it was as low as it was in March was in 2005.

“The lack of inventory is a reminder of the need for more housing to meet the continued strong demand,” Kim said.

The state Department of Business, Economic Development and Tourism issued a report last year projecting that about 65,000 new homes statewide would be needed to keep pace with population growth over 10 years, or 6,500 annually, while closer to 3,000 homes a year have been built in recent years. Most of the new housing — more than 25,000 homes — would be needed on Oahu.

The University of Hawaii Economic Research Organization published a report in February that projects median Oahu home prices will make single-digit percentage point gains to set new records this year, and that the modest gains would push the median single-family home price close to $800,000 by next year while the median condo price would top $400,000.

“Home prices continue to mount, but at a fairly restrained pace,” the report said.