Investors await the Fed's Sept. 12-13 meeting to see whether the central bank decides to take any action after Friday's disappointing US employment data. Steps could include a third round of quantitative easing, or QE3, or an extension of the period for which the Fed has committed to keep rates near zero, which now goes through late 2014.
US nonfarm payrolls grew by 96,000 jobs in August, sharply below the 125,000 forecast.
The US yield curve steepened after the jobs data as longer maturities underperformed due to investor concerns about potential inflation from additional easing.
"The US jobs report was bad, but longterm debt wasn't really bought in US time on Friday," said Ayako Sera, senior market economist at Sumitomo Mitsui Trust Bank in Tokyo.
The yields on the 10-year notes dropped to 1.643 percent from 1.664 percent in late U.S trading and from 1.678 percent in Asian trade on Friday. Immediately following the jobs data, they fell as low as 1.59 percent.
US debt prices were also underpinned in Asian trading by weaker-than-expected Chinese trade data. China's exports in August grew less than forecast while imports dropped.
Yields on five-year notes slipped to 0.623 percent from 0.641 percent in Friday's late US trading. That tenor posted gains on Friday on expectations that the Fed will focus any new bond purchases on mortgage-backed debt of the same duration.
The yield on the 30-year bond fell to 2.80 percent from 2.82 percent in US trading on Friday.
Investors are also watching developments in Europe, after the European Central Bank unveiled a potentially unlimited bond-buying programme last week which will focus on short-dated bonds, aiming to cap soaring yields in countries like Spain and Italy.
On Wednesday, Germany's Constitutional Court is scheduled to issue a key ruling on whether the euro zone's bailout fund is compatible with German law, and the Netherlands will hold elections.
On the supply front, the Treasury will sell $66 billion in new supply, including $32 billion in three-year notes on Tuesday, $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday.