Coming off a day of price declines with traders focused on auctions of new government debt, Treasury price gains on Tuesday were strongest among longer maturities.
The 30-year bond climbed well over 2 full basis points in price and was last up 1-30/32 to yield 2.8062, a level last touched on May 4.
"People seem to be trading this as a reason for Fed delay," said Michael Wallace, global market strategist at Action Economics in San Francisco. "This puts the Fed tightening horizon back on the table in terms of discussion."
The Fed has been largely seen as ending an era of near-zero short-term rates sometime in 2015, with a first hike in almost a decade possibly coming in September.
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But policymakers, who appear to be focused on U.S. labor conditions and inflation as key prompts for launching rate increases, may delay out of concern of hurting global economic growth.
Treasurys briefly trimmed gains when the government reported U.S. non-farm productivity as rebounding in the second quarter, but the data came with a weak underlying trend suggesting inflation could accelerate more than economists have anticipated.
The benchmark Treasury 10-year note was last up 27/32 and last yielded 2.1391 percent after closing on Monday at 2.238 percent. It had traded up over 1 full point and yielded as little as 2.1140 percent, its lowest since June 1.
The 7-year was up 20/32 in price, carrying a yield of 1.8894 percent that was last seen in late June.
Separately, the Treasury Department sold $24 billion of three-year notes, with indirect bidders purchasing their highest share in more than 5-1/2 years. The deal had a high yield of 1.013 percent.