* Traders unwind Ukraine bids before Friday payroll data
* U.S. jobless claims tumble to three-month low
* U.S. seen selling $64 billion coupon debt next week
* Fed to buy $1 bln to $1.25 bln debt due 2036-2044
NEW YORK, March 6 (Reuters) - U.S. Treasury debt prices fell on Thursday as investors unwound safe-haven bids spurred by the Ukraine crisis ahead of Friday's key nonfarm payrolls report and following data showing fewer Americans than expected filed new claims for jobless benefits.
Investors finished reducing their bond holdings on the Ukraine crisis as they looked ahead to results from a referendum vote due in 10 days that will decide whether Crimea will become a part of Russia.
"German Bunds were sensitive to the Ukraine situation and sold off a bit. Treasuries and other safe havens have followed," said Steve Van Order, a fixed income strategist with Calvert Investments in Bethesda, Maryland.
Wednesday's weak private employment data and a severe winter have clouded predictions for Friday's unemployment report, said Van Order.
"You could have almost anything come out tomorrow," he said.
The number of Americans filing new claims for unemployment benefits hit a three-month low last week, a sign of strength in a labor market that has been hobbled by severe weather. That sent yields to a session high of 2.7410 percent.
Losses were capped by the European Central Bank's decision to leave interest rates unchanged, holding its nerve in the face of uncomfortably low inflation.
Ten-year notes were last down 14/32 in price, pulling yields up to 2.745 percent after Wednesday's close of 2.696 percent. Thirty-year bonds fell 22/32, sending yields to 3.682 percent from Wednesday's close of 3.644 percent.
Traders see 10-year note yields finding support at 2.75 percent, the 100-day moving average and resistance at the 2.60 percent.
The Federal Reserve will buy between $1.00 billion and $1.25 billion of debt maturing between 2036 and 2044.
At 11:00 a.m. (1600 GMT), the Treasury will announce the size and date of auctions for three-month and six-month bills as well as three-year, 10-year and 30-year bonds next week.
Analysts forecast the Treasury will sell a combined $64 billion in three-year, 10-year and 30-year debt.