TREASURIES-U.S. bond yields rise on hopes of Greek deal

* U.S. Treasuries market set for worst quarter since 2010

* Conflicting reports on Greece debt deal before referendum

* Weaker-than-expected U.S. data support bids for U.S. bonds

* U.S. economy near full employment - Fed's Fischer

(Recasts throughout, adds closing prices)

By Richard Leong

NEW YORK, June 30 (Reuters) - U.S. Treasuries yields rose on

Tuesday, closing a rough quarter, as hopes of a last-minute deal

between Greece and its creditors that would keep the

cash-strapped nation from leaving the euro zone pared the

safe-haven demand for U.S. government debt.

The Treasuries market was on track to post about a 1.5

percent loss in the second quarter, which would be its worst

quarter since the final three months of 2010, according to an

index compiled by Barclays (LSE: BARC.L - news) .

In choppy trading, U.S. benchmark yields bounced up from

one-week lows set during Monday's rally due to a weekend

breakdown in talks between Athens and international lenders

ahead of Tuesday's deadline for Greece to repay the

International Monetary Fund $1.77 billion.

The contentious, unpredictable negotiations have resulted in

investors piling in and out of Treasuries and other low-risk

assets in recent days, analysts said.

"It's all about Greece. The Treasuries market seems to be

trading on each Greece headline," said Thomas Roth, executive

director of U.S. government trading at Mitsubishi UFJ Securities

USA in New York.

On Tuesday, European Commission President Jean-Claude

Juncker made an offer to convince Greek Prime Minister Alexis

Tsipras to accept a bailout deal he has rejected before a

referendum on Sunday which EU partners say will be a choice of

whether to stay in the euro.

These latest developments were mitigated by

weaker-than-expected U.S. domestic economic data, including a

weaker-than-expected rise in home prices in April, according to

S&P/Case-Shiller, and a smaller-than-expected increase in a

private measure on business activity in the Chicago area.

Month-end related buying and news of German Chancellor

Angela Merkel ruling out new debt talks until after Sunday's

referendum briefly sent the Treasuries market into positive

territory until demand faded in late trading.

Bond selling re-emerged after Federal Reserve Vice Chairman

Stanley Fischer said the U.S. economy is approaching full

employment, supporting the view the central bank would raise

interest rates later this year.

Benchmark 10-year Treasuries notes were down

5/32 in price for a yield of 2.351 percent, up 2 basis points

from Monday. The 10-year yield was up 42 basis points in the

quarter, the steepest quarterly rise in two years.

The 30-year bond was down 16/32 in price for a

yield of 3.125 percent, up nearly 3 basis points. The 30-year

yield was up 58 basis points in the quarter, the largest

quarterly yield rise since the fourth quarter of 2010.

(Reporting by Richard Leong; Editing by Dan Grebler)