WASHINGTON (Reuters) - The number of Americans filing first-time claims for unemployment benefits plunged last week to a level not seen since before the 2001 recession, the government said on Thursday, fueling hopes a long slide in employment had ended.

Coupled with other recent news indicating an improving labor market, the data suggested a quickening pace of recovery had finally taxed the ability of businesses to boost production without hiring workers, economists said.

"The odds ... do increasingly favor a revival in job creation," Federal Reserve Chairman Alan Greenspan said in cautiously upbeat remarks that nevertheless stopped short of declaring a sustained pickup in employment had arrived.

Greenspan told the Securities Industry Association "a notable pickup in hiring" was possible if businesses found a need to rebuild depleted inventories and were unable to squeeze new efficiencies out of their operations.

The economy surged ahead at a 7.2 percent annual rate in the third quarter -- the fastest pace in nearly two decades -- but employment dropped by 41,000 as businesses met rising demand by boosting productivity, or worker output per hour.

The Labor Department's report on Thursday, though, said initial claims for state unemployment aid fell 43,000 to 348,000 in the week to Nov. 1 from a revised 391,000 the prior week. The unexpectedly steep tumble took claims to their lowest since late January 2001, two months before the recession.

On the productivity front, the department said in a separate report that non-farm business productivity climbed at an 8.1 percent annual rate in the third quarter, the biggest surge since the first quarter of 2002.

But economists said last quarter's productivity rise was unsustainably strong and the drop in jobless claims, and a report early last month that showed payrolls rose by 57,000 in September, signaled firms had already found a need to hire.

"The fact we're beginning to see increases in payrolls suggests that firms are in fact finding productivity gains harder to come by," said Jade Zelnik, chief economist at RBS Greenwich Capital Markets. "The large drop in claims ... confirms that firms have begun to hire and employment has turned up." The upbeat data was little help to stock prices, which were up slightly in late afternoon, but the dollar rose.

At the same time, prices for U.S. Treasuries initially plunged as investors bet the data brought nearer an eventual interest rate hike by the Federal Reserve.

However, Treasury prices came back a bit after Greenspan delivered his remarks, in which he said the Fed could afford to be "more patient" because of low inflation.