U.S. Treasury yields inched lower on Tuesday as investors considered the path ahead for inflation and interest rates following a series of remarks from Federal Reserve speakers.

At 4:01 p.m. ET, the yield on the 10-year Treasury was down by more than 2 basis points to 4.412%. The 2-year Treasury yield was last at 4.831% after slipping by less than one basis point.

Yields and prices move in opposite directions. One basis point equals 0.01%.

Investors assessed the state of the economy, especially regarding inflation, and how this may affect interest rates.

Several Federal Reserve speakers reiterated caution about inflation and whether it is headed back toward the central bank's 2% target range.

Fed Governor Christopher Waller said Tuesday that he'd like to see more good data on the inflation front before lowering rates.

"The economy now seems to be evolving closer to what the Committee expected," Waller said. "Nevertheless, in the absence of a significant weakening in the labor market, I need to see several more months of good inflation data before I would be comfortable supporting an easing in the stance of monetary policy."

Earlier this month, the consumer price index for April reflected price increases of 0.3% on a monthly basis and 3.4% from a year ago. The monthly figure was just below estimates, while the annual reading was in line with expectations.

"We will need to allow our restrictive policy some further time to continue its work," Barr said.

This comes as uncertainty about when the Fed may start cutting rates has lingered among investors. Traders are looking ahead to the minutes from the Fed's April 30-May 1 meeting, which will be issued on Wednesday.

On the data front, existing as well as new home sales figures and durable goods orders data are due this week.