Benchmark 10-year notes last rose 29/32 in price to yield 1.3738%, from 1.47% late on Friday. The 30-year bond touched a record low yield of 1.811.
In currency markets the Japanese yen strengthened 0.77% to 110.74 per dollar. The dollar index fell 0.13%, with the euro up 0.08% to $1.0852.
"Ultimately this is all a risk-off trade," said Marvin Loh, senior global markets strategist at State Street Global Markets.
"When you look at the yen, when you look at the Swissie, when you look at rates, it is risk-off. It's probably reflective, to a certain degree, of the market being a little too sanguine up until now ... so there's an adjustment process around it."
Korea's won was down 1% and emerging-market currencies, from Mexico's peso and Turkey's lira to Poland's zloty and Russia's ruble, were all in the red.
Oil pared some of its early losses. U.S. crude fell 3.8% to $51.35 per barrel and Brent was last at $56.18, down 3.97% on the day. Both had fallen more than 5% during Monday's session.
Among the main industrial metals, copper lost 1.33 percent to $5,688.50 a tonne.
"As the virus spreads globally, additional downside revisions in oil demand for this year may be required," Jim Ritterbusch, president of Ritterbusch and Associates, said in a note.
"The accelerated sell-off in the stock market has become difficult for the oil market to ignore," he said.
Yields on top-rated, tax-exempt U.S. municipal bonds fell to all-time lows of 1.01% in 10-year paper and 1.6% in 30-year debt, according to Municipal Market Data.
