WASHINGTON — The number of borrowers falling behind on their mortgage payments dropped sharply at the end of last year, a sign the foreclosure crisis is beginning to ebb.

The Mortgage Bankers Association said Friday that the percentage of borrowers who missed just one payment on their home loans fell to 3.6 percent in the October to December quarter, down from 3.8 percent in the third quarter. The decline was even more surprising because delinquencies usually rise at that time of year due to higher heating bills and holiday spending.

The new trend in late payments is significant because it means the number of people going into foreclosure will continue to decline this year. And that is important for all homeowners in areas where cheaply priced foreclosures are bringing down neighboring values.

In high-foreclosure cities like Las Vegas, Phoenix and Miami, for example, homes have lost roughly half their values from their peaks. But today’s report showed Nevada, Arizona and Florida had some of the biggest declines in new delinquencies.

Jay Brinkmann, the trade group’s chief economist, said the report likely marks “the beginning of the end” of the wave of mortgage delinquencies and foreclosures that started more than three years ago.

Still, more than 15 percent of homeowners with a mortgage have missed at least one payment or are in foreclosure, a record for the 10th straight quarter.

“The bad news is that we still have a big problem,” Brinkmann said. “The good news is it looks like it may not get much bigger.”

There will be, however, more short-term pain. Nearly half of all delinquent borrowers were at least three months behind on their payments, up from a typical level of under 20 percent.

Banks have prolonged the foreclosure process, traditionally between four and six months, as they evaluate borrowers for help under the under the Obama administration’s $75 billion mortgage relief effort. It lowers borrowers payments to as low as 2 percent for five years and extends loan terms to as long as 40 years.

But experts warn that hundreds of thousands of borrowers won’t be eligible or won’t complete the process. So far, only 116,300 borrowers out of about 1 million who enrolled have had the terms of their mortgages changed permanently.

Obama, meanwhile, was to announce Friday that housing agencies in the five hardest-hit states will receive $1.5 billion to help spur local solutions. Those five are Arizona, California, Florida, Michigan and Nevada.