By Lisa Lambert

WASHINGTON (Reuters) - The supply of unsold new U.S. homes plummeted in March in the biggest drop in more than 45 years, government data showed on Friday, offering hope the distressed housing market is stabilizing.

A separate report on durable goods orders showed weakness persists in manufacturing, and possibly the economy as a whole, but analysts seized on the 5.2 percent drop in housing inventory as a bright spot.

"Housing is probably forming a bottom, because even the supply of homes, the inventories, declined," said Asha Bangalore, an economist with Northern Trust in Chicago. "I think the housing market is stabilizing."

As they work on decreasing supply, builders also appear to be holding off on adding new homes. A separate Commerce Department report showed applications for permits to build new homes were off 8.5 percent in March from February and 44.6 percent from March 2008.

That seemed to be the key factor in the reduction in inventories, as buyers have not snatched up increasingly affordable homes despite the median new home price dropping to $201,400 from $208,700. The Commerce Department said March sales slipped 0.6 percent.

But February sales were much stronger than originally thought. The report showed they rose 8.2 percent, compared with the 4.7 percent gain previously registered.

A revision to the March sales numbers will be released next month.

Inventory levels have plunged a record 33.7 percent since March 2008, and the supply of homes available for sale shrank to 10.7 months' worth in March from February's 11.2 months.