Yields near lows as ECB adjusts haircuts for Greece

U.S. Treasury tumbled on Monday after the European Central Bank said it would maintain emergency assistance for Greek banks, but adjusted haircuts on collateral.

Yields inched toward session lows after the report after paring losses after a report showed U.S. service sector growth inched higher in June.

The Institute for Supply Management said its services sector index increased to 56.0, just short of analysts' expectations of 56.2 in a Reuters survey, from 55.7 in May. A reading above 50 indicates expansion in the sector.

Prices rallied earlier, pushing yields lower, after a surprise "no" vote in a Greek referendum on the country's bailout terms fueled fears of Greece exiting the euro zone and boosted demand for safe-haven bonds.

The yield on the benchmark 10-year Treasury fell about 9 basis points to about 2.29 percent—its lowest level in over two weeks. The 30-year bond yield was down 10 basis points at about 3.08 percent.

The "risk off" mood in global markets following Sunday's Greek referendum also lifted German Bund prices, but dealt a blow to stocks with European markets lower and U.S. stock futures also trading in the red.

Read More'Toxic' Varoufakis is out: Time for a deal?

"Global markets did not take it (the Greek vote) well… the risk off trade sets the market tone for now," Bill Blain, a strategist at Mint Partners in London, said in a note.

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U.S. markets were closed on Friday for the Independence Day holiday, re-opening on Monday to another week that is likely to be dominated by Greece.

The country's outspoken Finance Minister Yanis Varoufakis, meanwhile, resigned on Monday, removing an obstacle to talks with Greece's creditors.

Greece has imposed capital controls, last week defaulted on a loan to the International Monetary Fund and is in desperate need of further aid to avert a bankruptcy.

Fed minutes eyed

Expectations for a September interest rate hike from the Federal Reserve have been scaled back after softer-than-expected U.S. jobs numbers last week and upcoming economic data are likely to be scrutinised for clues on the timing of a rate rise.

Minutes from the Fed's June meeting are released on Wednesday, while Fed chief Janet Yellen is scheduled to make a speech on the U.S. economic outlook in Cleveland, Ohio, on Friday.

Read MoreWhen markets get past Greece, they'll watch Yellen

"There will be particular interest in the FOMC (Federal Open Market Committee) debate on the policy outlook and their specific areas of concern in terms of what might push back rate lift-off, or indeed what might bring the timeline forward," Marc Ostwald, a strategist at ADM Investor Services, said in a note, referring to the Fed minutes.

"While incoming data since the June 17 press conference seems unlikely to have altered Yellen's assessment of the economic outlook, her speech on Friday will be closely watched for any nuanced changes of emphasis."

—Reuters contributed to this report.