US benchmark West Texas Intermediate fell 5.3% to trade at $20 a barrel, while international benchmark Brent crude was off 6.5% at $23.
The falls came after the death toll from the pandemic surged past 30,000 at the weekend as cases in hard-hit Europe and the United States showed no sign of letting up.
Senior US scientist Anthony Fauci estimated the virus could possibly result in 100,000 to 200,000 deaths in the United States, while President Donald Trump extended "social distancing" guidelines until April 30.
The president also said he expected the country to "be well on our way to recovery" by June 1 – dropping his previous target of mid-April.
The virus has infected more than 140,000 in the world's top economy and left more than 2,400 dead.
At the end of last week, Riyadh said it had not been in touch with Moscow about potential output cuts while Russia's deputy energy minister said oil at $25 a barrel was not a catastrophe for the country's producers – signaling the two sides are still far apart.
"Demand concerns are critical but well known, what really took the market down were the signals we got from Saudi Arabia and Russia that they intend to continue their current path," Vivek Dhar, a commodities analyst at Commonwealth Bank of Australia, told Bloomberg News.
"Market hopes of a deal have come undone."
There are fears the commodity could fall further as storage tanks around the globe approach full capacity.
"When the storage capacity is filled, we should probably expect a response from Saudi Arabia, Russia, and other essential oil producers," AxiCorp's Stephen Innes said, though he warned "the longer their response takes, the higher the risk of another steep decline in oil prices."