Ten-year Treasuries dipped 3/32 in price to yield 1.597 percent, up roughly 1 basis point from late US trade on Monday.

Treasuries had rallied on Monday on data showing that US manufacturing shrank in June for the first time in nearly three years, a reading that provided a stark sign of the economic recovery's slowdown.

With investors worried about downside risks to economic growth both in the United States and globally, the 10-year yield could head lower if inflation expectations were to decline, said a trader for a European brokerage in Tokyo.

US jobs data on Friday could become the catalyst for such a move, the trader said. The 10-year yield may head lower if the jobs data comes in weak and heightens concern about the economy's outlook, he said.

"In that case, expected inflation could drop and trigger a fall in yields," he said, adding that the 10-year yield may head toward a record low of 1.44 percent hit on June 1 under that scenario.

In any event, the 10-year yield seems unlikely to climb back above 2.0 percent in the near term, given worries about downside risks to the global economy, the trader added.

The 10-year Treasury yield has been trading in a range of 1.56 percent to 1.73 percent since early June.