US yields fell earlier on safe-haven bids stoked by a deadly suicide bombing in Britain.
The Treasuries market held in a tight trading range for a second day in the absence of major news or data to alter traders' expectations the Federal Reserve may raise interest rates at its June 13-14 policy meeting, analysts said.
"We are just chopping around sideway," said Blake Gwinn, US rates strategist with NatWest Markets in Stamford, Connecticut. "There's not a lot of investor conviction."
The benchmark 10-year Treasury yield was 2.269 percent, up over 1 basis point from late on Monday, while the 30-year yield was 1 basis point higher at 2.926 percent.
They hit session lows overnight but held above near last week's one-month lows in the aftermath of news that at least 22 people were killed and 59 injured in a suicide bombing at a concert hall in the English city of Manchester late Monday evening.
Interest rates futures implied traders saw about a 79 percent chance of a rate increase at the Fed's policy meeting next month, nearly unchanged from Monday, CME Group's FedWatch showed.
Earlier safe-haven bids faded a bit on selling in Treasuries and Bunds after a private survey showed German business confidence reached a record high in May and another survey suggested a solid pace of business growth in the euro zone this month.
The fall in US yields was limited by this week's corporate bonds supply, analysts said.
Companies raised $20 billion in the investment-grade bond market on Monday, with another $15 billion seen hitting before a three-day US holiday weekend, according to IFR, a Thomson Reuters unit.
The US bond market will close early at 2 p.m. (1800 GMT) on Friday and will be shut on Monday for the Memorial Day holiday.
Some analysts raised caution about the demand for the upcoming two-year Treasury issue as it seems expensive considering the possibility of a rate increase next month.
"It appears to be extremely rich," Gwinn said.
In "when-issued" activity, traders expected the new two-year issue to sell at a yield of 1.296 percent, which would be the highest yield since September 2008, Tradeweb data showed.