Applying the output cuts is essential Opec has argued
The price of crude oil has fallen below $64 a barrel on expectations that demand will continue to slow as the world economy contracts.
US light, sweet crude fell $3.87 to $63.91 a barrel, while in London Brent crude declined $4.84 to $60.48.
The oil cartel, Opec, recently decided to cut output by 1.5 million barrels per day in a bid to shore up prices.
However, the price of oil has continued to fall sharply from its record of more than $147 a barrel in July.
"Demand concerns haven't gone away so that's a factor that is weighing on the oil price," said David Moore, a commodities strategist at the Commonwealth Bank of Australia.
BP chief executive, Tony Hayward, said on Monday that demand in the US had slowed sharply in the wake of the economic contraction.
Preliminary data showed US demand was 2 million barrels a day lower in the last four weeks, compared to the year before, he said.
Reports suggest Kuwait and Nigeria have told customers that they have applied supply cuts already, but Saudi Arabia, the world's biggest oil exporter, has yet to tell its customers of output reductions.
Over the weekend Chakib Khelil, the head of Opec, said Saudi Arabia's implementation of the cuts was essential for the success of any output reductions.