S&P downgraded the country's long-term credit rating from CCC to CCC- with a negative outlook. The ratings agency said it saw a 50 percent probability that Greece would exit the euro zone.
Read MoreGreece latest: Pleas for help, protest in Athens
The bond market stabilized on mild profit-taking after earlier gains, although analysts anticipated volatile trading ahead of the end of the second quarter.
"The coast is not clear ahead of quarter-end," said George Goncalves, head of U.S. interest rates strategy at Nomura Securities International in New York. "There is still a belief there's a solution (for Greece) even though I think it's misplaced."
Amid worries Greece might eventually exit the euro zone, the Greek government shut banks and imposed capital controls, and Prime Minister Alexis Tsipras called for a referendum on Sunday on austerity cuts in the aid package proposed by creditors.
In addition to the Greece quagmire, investors are looking toward a batch of top-tier economic data, including the government's June payrolls report. The latter may reinforce ideas that the U.S. Federal Reserve might raise interest rates as early as September, the first such hike in about ten years.
"If you get another big jobs number, it would put a Fed rate hike in play," said Bret Barker, portfolio manager at the TCW Group in Los Angeles.