TREASURIES-Long bond prices rise with focus on auctions this week

* U.S. three-year note auction draws healthy demand

* Kocherlakota says Fed can be patient on rates

* Focus on upcoming supply (New (KOSDAQ: 160550.KQ - news) throughout, updates prices and market activity, adds details of 3-year note auction results, comments)

By Gertrude Chavez-Dreyfuss

NEW YORK, April 7 (Reuters) - U.S. Treasury long debt prices rose on Tuesday as investors consolidated positions in a week generally thin on economic data after last Friday's unexpectedly soft U.S. jobs report.

U.S. 30-year government bond prices, which move inversely to yield, were up sharply. Analysts said investors were adding to so-called "curve-flattening trades," reflecting expectations that short-term interest rates will rise at some point, but not imminently as inflation pressures remain muted.

"Friday's session got a little too rich with sharp gains in prices after the jobs report and we're still correcting from that," said Kim Rupert, managing director of global fixed income at Action Economics, in San Francisco.

"Other U.S. data aren't really corroborating the weakness that we saw in the payrolls report."

Minneapolis Fed President Narayana Kocherlakota, who is not a voting member on the Federal Open Market Committee, echoed the Fed's dovish stance. He said the Fed could afford to wait until well into next year to raise rates with the U.S. economy still years away from normal levels of inflation and employment.

The Treasuries market reacted little to Kocherlakota's remarks.

"The market has come to a point where it's comfortable understanding where the Federal Reserve is headed, that they are...data-dependent," said George Goncalves, head of U.S. rates strategy at Nomura Securities International in New York.

In late trading, U.S. 10-year prices were up 5/32 to yield 1.883 percent, from 1.900 percent late Monday. U.S. five-year notes were down 2/32 with a yield of 1.321 percent.

U.S. 30-year Treasuries were up one point in price, yielding 2.517 percent, from 2.553 percent on Monday.

The U.S. three-year note auction on Tuesday drew decent demand, with the government paying a lower yield than expected.

Bids totaled $78.1 billion for a 3.25 bid-to-cover ratio, although that was below last month's 3.33 and 3.30 average.

Indirect bidding, reflecting demand from foreign central banks, remained healthy, at 49.4 percent. That was lower from 51.4 percent last month, and higher than the 37.2 percent average.

On Wednesday, the market gears up for more supply, with the auction of $21 billion in 10-year notes. The U.S. Treasury Department then sells $13 billion in 30-year bonds on Thursday.

Overall, CRT Capital said Treasuries had an average day in terms of volume at 96 percent of the 10-day moving average. (Reporting by Gertrude Chavez-Dreyfuss; Editing by David Gregorio)