WASHINGTON — Single-family home construction posted a modest rebound in April, raising hopes that the three-year slide in housing is leveling off. But a bulging supply of unsold homes, record levels of foreclosures and still-falling home prices suggest a sustained recovery isn't likely until next spring at the earliest.

The Commerce Department said construction of homes and apartments fell 12.8 percent last month to a seasonally adjusted annual rate of 458,000 units. That's the lowest pace on records going back a half-century.

Applications for new building permits dropped 3.3 percent to an annual rate of 494,000, also a record low.

"I think we have probably reached the low point for this housing crash, but I don't expect us to come roaring back," said Mark Zandi, chief economist at Moody's Economy.com. "I think it will take another year for a recovery in housing to get going."

All of last month's weakness came in the volatile multifamily part of construction. By contrast, single-family construction and permits both rose, which economists took as a hopeful sign that this bigger sector of home construction was stabilizing.

That would be crucial for the broader economy. The recession — the longest since the Great Depression — was triggered by a collapse in the housing market that led to soaring loan losses and a grave crisis for the banking system. A healthy home market is needed to feed an economic recovery.

Many economists say home construction likely will stop falling in the current quarter. But any rebound isn't expected to take hold until next spring, and even then is likely to be slow. The reasons are the huge overhang of unsold homes, a wave of mortgage foreclosures and persistent job losses.

With foreclosures and other distressed properties for sale at deep discounts, builders often can't compete. Rather than launching new developments, they are waiting for signs of a broader recovery.

"They're being really cautious," said Michelle Meyer, an economist with Barclays Capital. "It will likely be a pretty gradual recovery in construction."

Zandi said he thinks home prices will keep falling until next spring and that sales won't start to show significant gains until the summer of 2010. And Wachovia economist Adam York said prices are likely to fall 10 percent more by mid-2010. Until then, the oversupply of homes is likely to remain a drag on the housing market.

The median price of a new home sold in March was $201,400 — down 23 percent from a peak of $262,600 two years earlier. The median price is the midpoint, which means half the homes sold for more and half for less.

The supply of unsold existing homes at the end of March fell 1.6 percent from a month earlier to 3.7 million, according to the National Association of Realtors, but still remained at elevated levels. With sales sluggish, it would take nearly 10 months to rid the market of those properties, compared with about 6.5 months in 2006, according to the Realtors data.

The government report Tuesday showed construction of single-family homes rose 2.8 percent in April to an annual rate of 368,000. That followed a 0.3 percent gain in March and no change in February.

Building permits for single-family homes rose 3.6 percent to a rate of 373,000 last month.

Multifamily construction plunged 46.1 percent to an annual rate of 90,000 units after a 23 percent fall in March. Permits for multifamily construction dropped 19.9 percent to 121,000 units.