Sunday's Greek election was likely to lead to a coalition government led by the conservative New Democracy, which beat the leftists who reject the austerity requirements of the 130 billion euro ($164 billion) bailout.
"The outcome (in Greece) means that the chances of the Fed easing because of European turmoil have faded, but weak US data last week means that the possibility of more easing remains, and that will give bonds some support," said Tomoaki Shishido, bond analyst at Nomura Securities.
Disappointing US economic data on Friday bolstered expectations that the Fed would take monetary stimulus steps at its policy meeting scheduled for Tuesday and Wednesday. It could either extend its "Operation Twist" stimulus programme, which expires this month, or launch a third round of asset purchases.
US factory production fell 0.4 percent in May and the Thomson Reuters/University of Michigan survey showed American consumer sentiment weakened to its lowest in six months in early June.
Investors were also watching developments from the Group of 20 summit in Mexico on Monday and Tuesday, where leaders initially welcomed the results of the Greek election.
The yield on 10-year notes rose to 1.65 percent from 1.58 percent in late US trade and 1.62 percent in Tokyo on Friday, moving further away a record low of 1.44 percent hit on June 1.
The yields on 30-year bonds stood at 2.76 percent, up from 2.69 percent in late US trade and 2.72 percent in Tokyo trade on Friday.