Treasurys were muted as the final week of June began, with investors set to zero in on Friday's key inflation report.
The 10-year Treasury yield was marginally lower at 4.246% on Monday. The 2-year Treasury yield was less than 1 basis point higher at 4.734%.
Yields and prices move in opposite directions. One basis point is equivalent to 0.01%.
With a summer interest rate cut from the Federal Reserve seemingly off the table, markets are hunting for more signs that September may be the month.
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That may come in the form of Friday's personal consumption expenditures price index, the Fed's preferred inflation gauge. The annual rate of price rises is expected to cool to 2.6% in May from 2.8% in April, according to Reuters.
Traders are currently pricing in a roughly 66% chance of a September cut, CME's FedWatch tool showed.
San Francisco Federal Reserve President Mary Daly on Monday said the central bank has made progress in its efforts to bring inflation down but can't let up yet.
Money Report
"We've made a lot of progress, but there is still work to do," Daly said in remarks for a speech in her home district. "Monetary policy is working, but we need to finish the job."
Other Fed officials are due to speak this week, including Governors Michelle Bowman and Lisa Cook, while data will roll in on house prices, new home sales, jobless claims and consumer confidence.
A final reading will confirm the rate of first-quarter growth in the U.S. economy, initially estimated at 1.6%.
