U.S. business productivity in the third quarter grew at the fastest pace in six years and new claims for jobless aid fell to a 10-month low last week, indicating the decline in labor market may be hitting bottom.

The Labor Department said on Thursday productivity surged at a 9.5 percent annual rate, the quickest pace since the third quarter of 2003, as companies squeezed more output from a smaller pool of labor to cut costs.

Analysts polled by Reuters had forecast productivity, which measures the hourly output per worker, rising at a 6.4 percent rate in the third quarter. Productivity grew at a 6.9 percent pace in the April-June period.

In another report, the department said initial claims for state unemployment benefits dropped 20,000 to 512,000 last week, the lowest since early January. Analysts polled by Reuters had forecast new claims slipping to 523,000 last week from a previously reported 530,000.

Productivity data has indicated resilience and growth, though it also has a negative connotation of more being done with fewer workers, said Peter Kenny, managing director, Knight Equity Markets in Jersey City, New Jersey.

As we go to a more efficient model, it'll take longer for us to reach full employment. Expect unemployment to creep up as productivity does.

U.S. stock index futures added to gains after the economic data, while the dollar pared losses against the yen.

Productivity in manufacturing rose at a record 13.6 percent rate in the third quarter. Total non-farm output rebounded, growing at a 4 percent rate in the July-September quarter after dropping 1.1 percent in the previous period.

Productivity has increased sharply over the past two quarters, largely driven by aggressive cost cutting by businesses.

Analysts see little room for more cuts and believe that this, coupled with the economy's resumption of growth in the third quarter, may cause companies to start increasing payrolls.

The Federal Reserve on Wednesday expressed optimism an economic recovery was building and was concerned the process would be sluggish as household spending remained constrained by job losses, low income growth and tight credit conditions.

The U.S. central bank left its benchmark overnight lending rate unchanged near zero and pledged to keep it there for an extended period.

The combination of very a powerful productivity gain and low labor costs ... keeps inflation at bay. This reinforces the Fed's ability to stay on the sidelines for an 'extended' period.' said Richard DeKaser, president, Woodley Park Research in Washington.

The economy grew at a 3.5 percent annual pace in the July-September period, probably ending the worst U.S. recession since the Great Depression of the 1930s.

In the weekly claims report, the four-week moving average for new claims slipped 3,000 to 523,750 last week, also the lowest in almost 10 months and declining for the ninth week in a row, indicating the labor market continues to edge toward stability.

The four-week moving average is considered a better gauge of underlying trends as it irons out week-to-week volatility.

While new applications for unemployment insurance have substantially fallen from March's high levels, they remain elevated and analysts say they need to drop below 400,000 to signal that the economy is creating jobs

The Labor Department is expected to report on Friday that the decline in employment is slowing. Analysts have forecast that payrolls fell 175,000 in October, compared with a decline of 263,000 in September.

Some healing of the labor market is crucial to sustaining and strengthening the economy's recovery after its worst recession in 70 years. The economy grew in the third quarter for the first time in more than a year, driven largely by the government's stimulus program.

There were further signs of labor market improvement, with the number of people collecting long-term unemployment benefits dropping 68,000 to 5.75 million in the week ended October 24, the lowest since March.

So-called continuing claims have stayed below the 6 million mark for a third successive week.

In sign that inflation pressures remained muted, unit labor costs, fell 5.2 percent last quarter after declining 6.1 percent in the second quarter. Analysts had expected unit labor costs to fall 4 percent in the third quarter.

Compensation per hour jumped at a 3.8 percent pace, but after adjustment for inflation, it was up only 0.2 percent.

Compared with the July-September quarter of 2008, non-farm productivity rose at a 4.3 percent rate. Unit labor costs fell 3.6 percent year-on-year.

(Reporting by Lucia Mutikani; Editing by Neil Stempleman)