Benchmark 10-year US Treasury yields were little changed at 1.91 percent. Overnight, those yields fell as far as 1.879 percent -- the lowest since at least World War Two.

There was no telling how far 10-year yields could fall, a trader said. "It's anybody's guess on the 10-year at the moment. We breached the 2 percent level so there doesn't seem to be a whole lot of resistance out there to stop this move," he said.

The trader expected a series of auctions this week to go smoothly against an increasingly risk-averse economic backdrop. The Treasury will sell $32 billion of three-year notes later on Monday, $21 billion of reopened 10-year notes on Tuesday and $13 billion of reopened 30-year bonds on Wednesday.

Bad news out of Europe was relentless. European share prices hit a 26-month low, partly on fears that France's top banks could be in for a credit rating downgrade from Moody's ratings agency.

There were also concerns a Greek debt default was becoming a real possibility: the country's deputy finance minister said on Monday Greece has cash to operate until next month and senior politicians in German Chancellor Angela Merkel's centre-right coalition have started talking openly about a Greek default.

"You have European officials allegedly contemplating that Greece could default, French bank woes, and potential downgrades ... the list is pretty long in terms of concerns," Charles Diebel, head of market strategy at Lloyds Bank said.

US 30-year government bond yields were little changed at 3.25 percent, and short-dated yields were virtually flat. Those bonds have been stuck in a range since the Federal Reserve said it would keep interest rates near record lows for some time.

Copyright Reuters, 2011