• The U.S. Bureau of Labor Statistics' February survey of job openings and labor turnover in the U.S. showed a slight increase in opening positions and hiring.
• Cleveland Fed President Loretta Mester told CNBC Monday that she welcomed the jump in payrolls in the March report, but said this wasn't enough for the central bank to change its policy.

U.S. Treasury yields dipped on Tuesday morning as the S&P 500 and the Dow Jones Industrial Average settled back below their record highs.

The yield on the benchmark 10-year Treasury note fell to 1.654% in afternoon trading. The yield on the 30-year Treasury bond slipped to 2.316%. Yields move inversely to prices.

The move lower in yields came as the stock market retrenched on Tuesday. The Dow, S&P 500 and Nasdaq all fell slightly.

The U.S. Bureau of Labor Statistics' February survey of job openings and labor turnover in the U.S. showed a modest increase in job openings and hiring on Tuesday. That data was from a period before last week's nonfarm payroll report, which showed more than 900,000 jobs added in March.

Indeed Hiring Lab's Nick Bunker said in a note that the report was positive for the economic recovery.

"This report is filled with optimistic signs," Bunker said. "Employers are increasingly ready to hire new workers, which is vital as employment is still down millions of jobs. Not only are job openings 5 percent above their pre-pandemic levels, significant hiring is finally taking place in some industries hit hardest by the pandemic."

Cleveland Federal Reserve President Loretta Mester told CNBC on Monday that she welcomed the jump in payrolls in the March report, but said this wasn't enough for the central bank to change its policy. Mester said she was largely unconcerned by the recent run-up in Treasury yields, given the improving economic outlook.

The Fed has indicated it will let inflation run above its long-range target of 2%, if it helps achieve full employment, despite market concerns sending bond yields higher.

Speaking to CNBC's "Squawk Box Europe" Tuesday, NN Investment Partners head of European equities Maarten Geerdink highlighted that average inflation targeting was "still very much set in the minds" of the Fed, so it wants to "see a bit of an overshoot because we have to compensate (for) periods of lower inflation historically."

An auction was held Tuesday for $40 billion of 42-day bills.

— CNBC's Jeff Cox contributed to this report.