Yields briefly fell earlier on Monday after a New York state manufacturing survey turned negative for the first time since October, adding to a recent string of weakening data.

Weaker-than-expected US consumer inflation data for April on Friday diminished the view that the Fed would raise interest rates more than once for the rest of the year.

Benchmark 10-year US bond yields have largely held in a range between around 2.20 percent and 2.40 percent since March 22 as investors wait on further clarity on whether the Trump administration is likely to pass tax and fiscal overhauls this year.

The measures are expected to boost economic growth, making further interest rate increases more likely.

"There are so many unknowns for us to really move in either direction," said Charles Comiskey, head of Treasuries trading at Bank of Nova Scotia in New York. "We are in a tight range until something occurs."

The 10-year notes  fell 3/32 in price to yield 2.34 percent, up from 2.33 percent late on Friday.

The yields fell to 2.32 percent overnight, the lowest since May 3, on safety buying after North Korea fired a ballistic missile that landed in the sea near Russia on Sunday.

Housing starts and industrial production data will be in focus on Tuesday.

Investors will also watch to see how much demand there is for a $11 billion reopening of 10-year Treasury Inflation-Protected Securities (TIPS) on Thursday, in light of the weaker inflation data.

"TIPS have been under pressure," said Justin Lederer, an interest rate strategist at Cantor Fitzgerald in New York.

Futures traders are pricing in a 69 percent chance of a June hike, down from 83 percent a week ago, according to the CME Group's FedWatch Tool.

The traders see only a 49 percent chance that two or more rate increases will be made by year-end.