"It is hard to imagine that yields will be rising much anytime soon, until there is more clarity on Europe's situation and the US fiscal cliff is resolved," said a fixed-income fund manager at a Japanese asset management firm.
Yields on 10-year Treasuries fell to 1.589 percent on Tuesday in Asian trade from 1.613 percent in late US trade on Friday. Yields on 30-year Treasuries eased to 2.717 percent from 2.751 percent.
There was no US trading of Treasuries on Monday due to the Veterans' Day holiday. It will reopen later on Tuesday.
Euro zone finance ministers gathered in Brussels gave Greece two more years to make the cuts demanded of it. But they not disburse more aid, and the euro zone and IMF clashed over a longer-term target date to shrink the country's debt pile.
A looming US fiscal crisis also underpinned bonds, as investors worried about the possible impact of about $600 billion in expiring tax cuts and spending reductions due to take effect in January. US lawmakers return to the capital on Tuesday to try to work toward a compromise.
Newly re-elected US President Barack Obama on Friday invited congressional leaders to the White House to start negotiating a deal, vowing to veto any bill that would extend tax cuts for the top 2 percent of wage earners.