TREASURIES-Bond prices back up on strong jobless data

* Long bond yields back away from record lows

* Treasury sells $64 billion of new debt

* Weekly jobless applications near 15-year low (Adds late prices, auction details and quotes)

By Michael Connor

NEW YORK, Jan 29 (Reuters) - U.S. Treasuries fell on Thursday, with long-term yields backing away from record lows as U.S. jobless claims figures shrank to a 15-year low and investors made room for $64 billion of new government debt.

After three days of price increases, the 30-year bond was last off 23/32 in price to yield 2.3281 percent. The bond hit a record low yield of 2.273 percent on Wednesday in a rally fueled in part by a Federal Reserve statement that inflation was running below forecasts.

The 10-year note was down 9/32 to lift its yield to 1.7597 percent. Other maturities were also mostly off, according to Thomson Reuters data.

Bond losses increased after the number of Americans filing new claims for unemployment benefits tumbled last week to its lowest since April 2000. It was also the biggest weekly decline since November 2012.

Some investors sold current holdings to make room for Thursday's five- and seven-year note auctions, said Jake Lowery, portfolio manager at Voya Investment Management in Atlanta (BSE: ATLANTA.BO - news) .

"Having the overlap of fives and sevens gave us a bunch of supply, and we had a very strong rally yesterday after the FOMC statement," said Natan Magid, rates strategist at BMO Capital Markets in New York. "Demand was strong for the auctions, despite the very low yield levels."

In the auctions, the U.S. Treasury Department sold $29 billion of seven-year notes at a yield of 1.590 percent and $35 billion of five-year notes at a yield of 1.288 percents. The yields were both auction lows not seen since May 2013.

Late on Thursday, prices on the five-year Treasury note were last off 6/32 to yield 1.2812 percent, while the seven-year was down 8/32 to yield 1.5698 percent. (Editing by Jonathan Oatis and James Dalgleish)