Treasury yields fell on Tuesday after Federal Reserve Chair Jerome Powell cited progress on squashing stubborn inflation.

The yield on the benchmark 10-year Treasury note fell more than 3 basis points to about 4.44%, while the yield on the 2-year Treasury note fell 3 basis points to trade at about 4.74%.

Yields and prices move in opposite directions, and one basis point is equivalent to 0.01%.

In his remarks at the European Central Bank Forum on Central Banking in Sintra, Portugal, Powell expressed satisfaction with the progress on inflation over the past year but said he wants to see more before being confident enough to start cutting interest rates.

"I think the last [inflation] reading and the one before it to a lesser, lesser extent, suggest that we are getting back on the disinflationary path," Powell said. "We want to be more confident that inflation is moving sustainably down toward 2% before we start the process of reducing or loosening policy."

The consumer price index, a broad inflation gauge that measures a basket of goods and services costs across the U.S. economy, showed no increase in May though it increased 3.3% from a year ago.

The Labor Department's Job Openings and Labor Turnover Survey, or JOLTS, released Tuesday showed openings changed little at 8.1 million, down by 1.2 million over the year.

The Fed's minutes from its latest policy meeting will be released on Wednesday, with U.S. nonfarm payroll data due on Friday.

— CNBC's Jeff Cox contributed to this report.