"That is one of the main reasons we are trading a bit better here ... there is more of a 'risk off' feel, given the headlines out of Greece," said Sean Murphy, a Treasurys trader at Societe Generale in New York.
Month-end extension buying added to price gains. "We have month-end extension coming up, and liquidity is going to be a concern with the holiday week," Murphy said.
Benchmark U.S. 10-year Treasury notes were last up 12/32 in price to yield 2.21 percent, down from 2.25 percent late Friday. The yield curve steepened after hitting six-and-a-half year lows on Friday as investors bet that intermediate-dated debt will continue to weaken compared with long-dated bonds.
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Short- and intermediate-dated notes are the most sensitive to interest rate increases and have been hurt as strong economic data raised expectations the Federal Reserve is closer to its first hike since the financial crisis. Thirty-year bonds have also been supported as a dearth of high quality assets leads investors to seek extended durations to reach for higher yields, and on concerns about deflation.
The yield curve between five-year notes and 30-year bonds was last at 106.20 basis points on Monday, up from 104.40 basis points on Friday. The next major focus for the market will be the release on Jan. 7 of minutes from the Fed's December meeting, when the central bank changed its vow to keep interest rates near zero for a "considerable time," to say that it would remain "patient."