Benchmark 10-year Treasuries yields fell to 1.84 percent, their lowest levels since Dec. 20, 2011 and down from 1.89 percent late Friday.

Portugal's debt protection costs hit new records and credit default swaps for other countries, including Spain and Italy, weakened on fears they would run into the same issues plaguing Greece.

Tensions between Greek and German leaders over whether Athens should maintain control of its budget also added to negative sentiment over the region.

"The main concern right now is if the situation in Greece will trickle out to Spain, or Portugal or Italy," said Jason Rogan, director of Treasuries trading at Guggenheim Partners in New York.

"These counties are much larger in size and the effects of them having similar issues to Greece will be much more worrisome" he said.

The Federal Reserve's statement last week that it will likely hold interest rates near zero until late 2014 added to Treasuries buying.

"The Fed gives people a lot more comfort in being long Treasuries, knowing that they are pretty much on hold for a very long time," said Rogan.

Treasuries were little moved after economic data showed US consumer spending was flat in December as households took advantage of the largest rise in income in nine months to boost their savings.