South Florida home prices continued a brisk march higher in March as eager buyers chased a dwindling supply of homes for sale, in most cases paying near the full asking price.

The median price of a single-family home in Miami-Dade County soared 25.1 percent to $225,000 in March from $179,850 a year earlier, the Miami Association of Realtors said.

The median price of a Miami-Dade condo jumped 19.3 percent year over year, to $167,000 from $140,000.

In Broward County, the median price of an existing single-family home rose 26.3 percent to $242,500 in March from $192,000 a year earlier, according to the Greater Fort Lauderdale Realtors.

The median price for townhouses and condos in Broward jumped 27.3 percent in March to $95,000 from $75,000 a year earlier.

Nevertheless, in Broward, as in Dade, prices remain sharply lower than their pre-recession peaks.

Miami-Dade, which was among the hardest-hit spots in the nation during the housing meltdown, has posted 16 consecutive months of price gains in both single-family homes and condominiums. Even with the rebound, the median prices in Miami-Dade are roughly at 2003 levels, well below the 2006 peak of $374,000 for a single-family home and $253,000 for a condo, according to EWM Realty International.

“It’s crazy out there, crazy,” said Liza E. Mendez, a broker and owner of Pedro Realty International in Hialeah, who recently listed a three-bedroom, three-bathroom townhouse in Miami Lakes for sale and drew 15 showings and four offers the first day. One of two cash offers prevailed over those planning on mortgage financing.

That’s a common theme. Would-be homebuyers consistently get shut out by those wielding cash.

“The Miami real estate market is experiencing comprehensive strengthening fueled by robust demand and limited supply,” said Natascha Tello, chairman of the Miami Realtors’ group. As a result, prices for a wide variety of homes — from bungalow to megamansion, suburban townhouse to urban flat — are leaping.

Even with a slim inventory, the number of Miami-Dade single-family home sales rose 6.1 percent to 1,022 closings in March from 963 a year ago. Condo closings in Miami-Dade were up 0.5 percent, essentially flat, with 1,458 closings in March compared with 1,451 a year ago.

Sales of single-family homes in Broward increased 2 percent to 1,199 closings during March from 1,175 a year earlier, the Greater Fort Lauderdale Realtors said. The increase in sales came despite a 24.5 percent plunge in the inventory of available single-family homes on the market in Broward in March compared with March 2012.

But with the inventory of Broward townhomes and condos for sale falling 8.9 percent year over year, the volume of sales dipped 2.9 percent in March from 1,499 closings from 1,544 a year earlier.

Judith Church Baker, managing broker of Prudential Florida Realty in Fort Lauderdale, said multiple offers on homes are increasingly common, and that cash is king.

“It’s challenging for people who are trying to get property with financing,” she said. “Buyers with [plans to take out] mortgages are fighting with buyers paying cash.”

Typically, sellers take a cash offer over one that entails financing — even if it is lower. That’s because lending standards remain strict, and appraisals often don’t keep pace with rising market prices.