U.S. government debt was back in favor after worries over European debt resurfaced with a warning about Greece's rescue package from a credit agency.
Traders bailed out of Treasurys last week as Greece passed bills that would give it access to emergency funds needed to avoid a default.
Standard & Poor's warned Monday that Greece would be considered to be in default if banks rolled over their holdings in the country's debt as France has proposed.
The price of the benchmark 10-year Treasury note rose 59.3 cents Tuesday for every $100 invested. Its yield fell to 3.12 percent from 3.19 percent late Friday. Bond yields rise when their prices fall. Bond markets were closed Monday in observance of Independence Day.
In other trading, the price on the 30-year Treasury bond was up 31.2 cents, sending its yield down to 4.38 from 4.39 percent late Friday.
The yield on the three-month T-bill was unchanged at 0.01 percent. Its discount was 0.02 percent.