Pledges of higher output from Saudi Arabia and Russia after a supply pact collapsed and a slide in demand due to the coronavirus outbreak have hammered the market.
Global benchmark Brent crude fell 66pc in the first three months of 2020, in its biggest ever quarterly loss.
As of 1217 GMT, June Brent was down 94 cents, or 3.6pc, at $25.41.
US West Texas Intermediate crude for May was down 11 cents at $20.37. Brent fell to $21.65 on Monday, the lowest since 2002, when the now-expired May contract was the front month.
"April will be one of the toughest months in history for oil and this is no April fool's joke," said Bjornar Tonhaugen of Rystad Energy.
"The market is oversupplied in April to the tune of 25 million barrels per day. There's nowhere to hide from this tsunami of oversupply."
Underlining supply glut fears, the American Petroleum Institute, an industry group, reported US crude inventories rose by 10.5 million barrels, far exceeding forecasts for a 4 million barrel increase.
Attention will focus on US government figures due on Wednesday to confirm the API figures.
The bearish mood was also fuelled by a rift within the Organization of the Petroleum Exporting Countries.
Saudi Arabia and other OPEC members have not agreed to hold a technical meeting in April to discuss sliding prices.
An OPEC-led supply deal fell apart on March 6 when Russia refused to cut output further. Saudi Arabia has already begun to boost output, a Reuters OPEC survey showed on Tuesday, and is expected to pump more in April.
"It is very unlikely that OPEC, with or without Russia or the United States, will agree a sufficient volumetric solution to offset oil demand losses," BNP Paribas analyst Harry Tchilinguirian said in a report on Tuesday.
US President Donald Trump said on Tuesday he would join Saudi Arabia and Russia, if need be, for talks about the fall in oil prices. Tonhaugen of Rystad was skeptical any new producer cooperation would do any good.
"Diplomacy won't be able to help the physical oil market nor oil prices in the short term," he said. "The market is officially broken and no longer reflecting the value of crude.