Matthew and Carina Hensley offered $10,000 more than the asking price for a three-bedroom house in suburban Seattle, then lost out to one of seven other bidders.

Their $270,000 proposal last month came with a family portrait and a letter introducing the couple, their 8-month-old daughter, Harper, and their desire to build a family in the Renton, Wash., house with a yard backing onto a woody hillside.

Bidding wars, absent from most parts of the U.S. residential market since its peak in 2006, are erupting from Seattle and Silicon Valley to Miami and Washington, D.C. The inventory of homes hovers close to a six-year low, while an increase in jobs and record affordability are tempting more buyers. The number of contracts to buy previously owned homes jumped 14 percent in February from a year earlier, the National Association of Realtors reported Monday.

“We understand there is going to be fierce competition in the offers made for your house, but Carina and I both felt very strong about letting you know what it would mean to us if we were given the opportunity to live in your gorgeous and charming house,” wrote Matthew Hensley, 33, a credit union branch manager whose wife is a dental hygienist. Such letters from eager buyers were common during the housing boom.

While listings will probably rise as banks accelerate foreclosures and sellers gain confidence in the market, the U.S. metropolitan areas with the strongest economies may be ready to absorb the additional inventory, said Mark Zandi, chief economist for Moody’s Analytics Inc. Low values and interest rates have made buying a better deal than renting in 98 of the largest 100 metropolitan areas, according to Trulia Inc.

“The housing crash is finally giving way to recovery in an increasing number of markets across the country,” Zandi said in an email. “The decline in unsold listings and vacant homes and the increase in rents presage better times ahead for single-family housing.”

The bidding wars seen in such places as Seattle aren’t found everywhere. In metropolitan areas including Atlanta and California’s Riverside and San Bernardino counties, housing remains weak as high unemployment and falling prices deter first-time and move-up homebuyers.

A contraction in supply hasn’t helped increase property values, which are down by a third from their July 2006 peak. Prices, hurt by discounted foreclosures and other distressed sales, will fall 2 percent more this year before rising 1.4 percent in 2013, according to a Moody’s Analytics projection.

A residential comeback would provide a boost to the U.S. economy. Housing will “contribute modestly” to the economy this year for the first time since 2005, according to Peter de Bruin, an economist at ABN Amro Group Economics in Amsterdam.

Rising demand for homes has cut into the supply, which is already low because many sellers — especially those with negative equity — are waiting for prices to increase before putting properties on the market.

About 2.43 million existing homes were listed for sale in February, the fewest for the month since 2005, the year U.S. home sales reached a record 7.08 million, the National Association of Realtors reported March 21. The number of listings rose by 100,000 from January, a seasonal bump that occurred every February since 2000 except for 2008, according to data collected by the Realtors.

The February supply of unsold homes listed for sale was down almost 50 percent from a year earlier in markets such as Miami, Phoenix and Oakland, Calif., according to Realtor.com, the National Association of Realtors’ official website.

The U.S. inventory of new homes stood at 150,000 in February, when new houses sold at an annual pace of 313,000, slower than analysts expected, the Census Bureau reported March 23.

The supply of new houses rose in January “as builders put inventory in place for the spring selling season,” Stephen East, an analyst with International Strategy Investment Group LLC in St. Charles, Mo., wrote in a note to investors. “This is the fourth consecutive month inventory has remained below six months’ supply, which is broadly considered supply/demand equilibrium.”

The new-home supply peaked in January 2009, forcing builders to book losses as the economy fell into recession. While the inventory has declined from that high, the housing market still has hurdles to overcome.

One hurdle for the residential market is the more than 11 million homes that had negative equity at the end of 2011.

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