Ten-year US Treasury yields were up 0.08 basis points at 1.60 percent but one trader said it could retest a record low of 1.44 percent over the next few weeks given the economic backdrop. Trade was thin a day before US independence day holiday, with the bond market also poised to close early this session.

US Treasury prices advanced on Monday as data showed the country's manufacturing sector contracted in June for the first time since July 2009. The data fuelled concerns about the economy's recovery, and analysts will look to non-farm payrolls data on Friday for further insight into its health.

"Markets are looking to that at the moment, because together the ISM manufacturing index and the non-farm payrolls are the main indicators of the US business cycle," Philip Marey, strategist at Rabobank said.  * The US economy is expected to have created 90,000 jobs in June, according to a Reuters survey, and anything between that and 70,000 would be expected by the market, Marey said.

"If it really goes below 69,000, I think that will be a big disappointment. It adds to the concern that the US recovery is faltering," Marey said.

The three-year-old euro zone debt crisis has also fuelled demand for safe-haven Treasuries, by hurting the global economic outlook.

"With all these surveys, the hardest part to know is if people aren't hiring because they are so worried about Europe. But the problem is we are not going to get a resolution in Europe (in the near-term), that's not going to go away," the trader said.

Riskier sovereign debt markets breathed a sigh of relief last week when European leaders agreed to a more flexible use of euro zone rescue funds, surpassing market expectations.

But the lack of details, concerns about whether the size of the fund was big enough for its new role, and Finnish and Dutch opposition limited the benefit of the deal for riskier assets. The Finnish government told parliament that Helsinki and its Dutch allies would block the euro zone's permanent bailout fund buying bonds in secondary markets.

Five-year government bond yields were down 0.05 basis points at 0.67 percent, while thirty-year US Treasury yields were 1.9 basis points higher at 2.71 percent.