Gains were muted, however, as investors continued to ponder how debt problems in Europe might play out after rating agency Standard & Poor's downgraded Greece's credit rating.
The US Treasury will sell $32 billion of three-year notes, $24 billion of 10-year notes and $16 billion of 30-year bonds on Tuesday, Wednesday and Thursday.
With investors looking for price concessions ahead of the sales, benchmark 10-year notes traded 4/32 lower in price to yield 3.16 percent, up from 3.15 percent late Friday, while 30-year bonds were 19/32 lower to yield 4.31 percent from 4.28 percent.
"Treasuries are slightly weaker as risk assets stage a mild rebound," said William O'Donnell, head of US Treasury strategy at RBS Securities in Stamford, Connecticut, noting that oil prices had recovered some of last week's sharp losses.
Yields have generally been climbing since early April as manufacturing and housing data pointed to a slowing in the economic recovery. Benchmark yields Friday touched the lowest since early December at 3.13 percent.
"Having hit the year's yield lows across the curve in a rather panicky sort of move over the last couple of weeks, a bit of a pause following the exhaustive covering rally is the thing we're going for," said David Ader, head of government bond strategy at CRT Capital Group in Stamford, Connecticut.
Two-year Treasury notes traded unchanged in price to yield 0.56 percent, while seven-year notes were also steady to yield 2.53 percent.
US stocks indicated a higher open, while crude oil futures rose about 2 percent.