Ten-year Treasuries rose around 3/32 in price to yield 1.640 percent, down 1 basis point from late US trade on Monday.
Investors are focusing on Bernanke's speech on Friday at a symposium in Jackson Hole, Wyoming for hints on whether the Fed will announce another round of bond-buying after its policy meeting on Sept. 12-13.
"I get the sense that it is hard to move in either direction," said Tomohisa Fujiki, interest rate strategist at BNP Paribas Securities in Tokyo, referring to the near-term outlook for Treasuries.
In the next few days, longer-term Treasuries may fare better compared to shorter-term debt and the yield curve may have a flattening bias due to the potential for month-end portfolio tweaking by investors, Fujiki added.
Investors sometimes buy longer-term Treasuries toward the month-end to extend the duration of their portfolios and to keep them in line with benchmark bond indexes.
Meanwhile, there will be a fresh supply of short-term and medium-term Treasuries this week, with an auction of two-year notes coming up later on Tuesday, followed by auctions of five-year and seven-year notes later in the week.