Brent LCOc1 fell $1.14 a barrel to $56.74, its lowest since May 2009, before recovering to trade around $57.20 by 0950 GMT.
U.S. crude CLc1 fell 60 cents to $53.01 after hitting $52.70 - also its lowest since May 2009. It fell $1.12 on Monday.
Oil markets have been oversupplied this year due to increasing output of high quality, light oil from U.S. shale and lower-than-expected consumption as a result of faltering global economic growth and competition from alternative fuels.
Several members of the Organization of the Petroleum Exporting Countries have suffered supply disruptions in recent months, but this has had little impact on prices.
In Libya, clashes between rival factions have closed oil ports and terminals this month, reducing exports from the OPEC producer, which used to sell over 1 million barrels per day of crude to world markets, to almost nothing.
OPEC, which pumps a third of the world's oil, had been expected to trim output to try to stabilise prices, but it decided in November to keep production unchanged and let the market find its own level.
PVM Oil Associates analyst Tamas Varga saw no let-up in the sell-off, saying "the bears" were in firm control of the market.
"The trend is still down and supports are expected to be under pressure. It is not recommended to go against this trend."
Reuters technical analyst Wang Tao said Brent may fall to $54.98, as it has resumed its downtrend, while U.S. oil is expected to drop to $52.10, as indicated by its wave pattern and a Fibonacci projection analysis.
Traders are now eyeing weekly U.S. inventory data.
An industry group, the American Petroleum Institute, is scheduled to release its report on Tuesday, while the U.S. Department of Energy's Energy Information Administration will release data on Wednesday.
A Reuters poll forecast that U.S. crude oil inventories will show a drop of 900,000 barrels last week. A draw would follow a rise to the highest recorded level for December in the week ended on Dec. 19.