The consumer price index (CPI) increased 0.3% last month after gaining 0.2% in December, the Labor Department's Bureau of Labor Statistics said on Tuesday. In the 12 months through January, the CPI increased 3.1%. Economists polled by Reuters had forecast the CPI gaining 0.2% on the month and 2.9% year-on-year.

The yield on the benchmark U.S. 10-year Treasury note on Tuesday rose 10 basis points to 4.273%. The yield on the 30-year bond rose 7 basis points to 4.437%.

"A slightly hot CPI really sent a chill down the spine of investors. The Fed doesn’t have a coherent set of criteria for cutting, so for all we know this resets the clock," said Brian Jacobsen, chief economist at Annex Wealth Management in Menomonee Falls, Wisconsin.

"If cutting is a confidence game, we don’t know when enough progress is enough or whether mild setbacks undermine their confidence. No wonder bond volatility is elevated."

After the data, expectations rose the Fed will likely not cut rates until June.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at a negative 32.8 basis points, from a negative 31.8 on Monday.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, rose 13 basis points to 4.599%.

• US Inflation Slows But Remains Elevated at 3.1%