New York's main contract, light sweet crude for delivery in February, dropped 92 cents to $35.59 a barrel.
The February contract expires at the close of trade Tuesday, to be replaced by the March contract currently at $41.59 per barrel.
In London, Brent North Sea crude for March slid $1.07 to $45.50 a barrel.
Underlying weak global demand for crude "remains a dominant factor" affecting the market, said David Moore, a commodity strategist for the Commonwealth Bank of Australia in Sydney.
Sucden Financial Research analyst Nimit Khamar added in London: "The US market holiday is likely to leave crude oil markets quiet, awaiting fresh news and even initiatives from the US as a new president and Congress come into office this week."
Wall Street was shut Monday for the Martin Luther King holiday.
Last week both the Organization of the Petroleum Exporting Countries (Opec) cartel and the International Energy Agency, energy policy adviser to major industrialised countries, lowered their demand forecasts for this year.
Opec, whose member nations together pump about 40 per cent of world crude, would consider further cuts to oil production if prices continued to fall, Algerian Energy Minister Chakib Khelil said Saturday.
Another cartel member, Venezuela, said at the weekend that it was prepared to reduce its oil production in a bid to boost prices.
"Only when Opec has implemented large-scale cuts will prices start to recover," Macquarie Research said in a report. It said the cuts would have to reach 3.0 to 3.5 million barrels per day, and said prices should start to recover in the second half of this year.
During the first six months, prices should range between $40 and $50 a barrel on the assumption that world oil consumption would fall and high stock levels would continue, Macquarie said.
World oil prices fell by about 54 per cent in 2008 as a sharp global economic slowdown dampened energy demand in the second half of the year. Prior to that, in July, crude futures had rocketed to record highs of above $147 a barrel on worries over tight supplies.