TREASURIES-Prices rise on prospects for sluggish recovery

*Treasuries prices up after Friday's sharp sell-off

*Buyers lured by 10-year yields near 3.40 percent

*Talk of restrained U.S. recovery aids safe-haven bid

*Fed Vice Chairman Kohn to speak about outlook

By Ellen Freilich

NEW YORK, Oct 13 (Reuters) - U.S. Treasury debt prices rose on Tuesday in line with euro zone bonds after a measure of German investor morale unexpectedly fell in October, adding to data that has curbed expectations for a strong economic recovery.

The most prominent report among the less promising data was the recent U.S. unemployment figures for September that revealed bigger-than-forecast job losses.

National Economic Council Director Lawrence Summers said on Monday that heavy job losses "cast a substantial shadow forward" and that lack of demand would be "a major constraint on output and employment in the American economy for the foreseeable future."

Dow index futures also erased early gains and turned slightly negative, putting a bit of polish on investors' preference for safe-haven U.S. government debt.

The firmer tone on Tuesday - the market was closed for Columbus Day on Monday - also followed a selloff Friday that followed an eight-week rally.

Benchmark 10-year notes US10YT=RR were up 15/32, their yields easing to 3.33 percent from 3.38 percent on Friday.

"The market has found a level - 10-year yields near 3.40 percent - where international investors care again," said Tom Di Galoma, head of fixed-income rates trading at Guggenheim Securities in New York. "We favor buying dips as the dollar declines."

EXIT OR NO EXIT

Recent intimations by some regional Federal Reserve officials that the central bank could raise interest rates even before the unemployment rate begins to fall also fed the view that a tighter monetary policy in the future could restrain the forward momentum of any recovery.

Even Federal Reserve Chairman Ben Bernanke said the U.S. central bank must continue to prop up the economy for an extended period but could not do so indefinitely for fear of triggering an inflationary surge.

As the debate continues, bond investors are likely to listen closely Tuesday afternoon for any clues to the Fed's eventual "exit strategy" from monetary ease when Fed Vice Chairman Donald Kohn speaks about the economic outlook to the National Association for Business Economics in St. Louis.

Fed Bank of New York President William Dudley is also due to speak before the Institute of International Bankers Fall Membership Luncheon at 1:15 p.m. (1715 GMT).

In early dealings, two-year notes US2YT=RR rose 2/32, their yields easing to 0.94 percent from 0.97 percent on Friday.

The 30-year long bond US30YT=RR was up 11/32 after falling more than two full points on Friday. Its yield eased to 4.20 percent from 4.22 percent on Friday. (Editing by Kenneth Barry)