But the outlook remains extremely uncertain and any signs that the pandemic is stabilizing should be viewed with utmost caution, analysts said.
Volume was light, with markets in Europe closed for Easter Monday and spurring choppy market action.
"The market wants to find confidence in some of the recent developments, but I still think it's going to be a very long slog," said Gennadiy Goldberg, senior rates strategist at TD Securities in New York.
"We may probably have weakness in earnings and that would be kind of a reminder that this is far from over and we will be still going through a period of extreme uncertainty," he added.
Over the weekend, major oil producers agreed to their biggest ever output cut. But crude prices fell on concerns even that would not be enough to head off oversupply with the coronavirus outbreak crushing demand.
On the pandemic front, a top US health official said on Monday the coronavirus outbreak could reach its peak in the United States this week, pointing to signs of stabilization across the country.
The United States, with the world's third-largest population, has recorded more fatalities from COVID-19 than any other country, more than 22,000 as of Monday morning, according to a Reuters tally.
Despite more positive news, risk appetite was off, with US stocks down on Monday.
"What seems apparent now is that many things can never be taken for granted," said David Rosenberg, chief economist and strategist at Rosenberg Research & Associates.
"The first is any notion that re-opening the economy is going to usher in a V-shaped recovery. It won't. That comes with either an effective treatment or a vaccine."
In mid-morning trading, US 10-year yields rose to 0.737pc from 0.722pc late on Friday.
Yields on US 30-year bonds were at 1.379pc , up from 1.348pc on Friday.
On the short end of the curve, US 2-year yields were last at 0.233pc , up from Friday's 0.225pc .