Opec is to wait till January 2002 to cut output.
Opec is desperate to boost the price of crude but has insisted on the support of other countries, especially Russia, Mexico and Norway.
Kuwaiti oil minister Adel al-Subaih said Opec would not implement its output cut - equal to 6% of output - unless non-Opec producers cut by 500,000 bpd.
"We all want non-Opec to contribute, including Russia," he said. "We cannot control the market anymore".
"If Russia does not cooperate with Opec there will be no cuts now or in the future," a senior Opec source told Reuters news agency.
Opec fears that even if it reduces supply from its members, the markets will still be flooded by oil from other producers.
That scenario would mean the revenue streams of Opec members would be substantially lowered despite their own sacrificial cuts.
Balancing the market
Russia has offered to cut production by a token 30,000 barrels per day (bpd), but Norway has denied that it has promised any reduction in production.
"The way I see the situation today there is no reason to implement measures," said Norwegian oil and energy minister Einar Steensnaes.
In London, benchmark Brent crude fell nearly $2 a barrel to hover just above a two-year low - it was trading at $18.90 a barrel within minutes of the news.
This compares with an average of $25.70 this year and the peak of $31.05.
Shoring up prices
Opec's aim is to shore up oil prices, which have lost one-third of their value since 11 September, as fears grow that demand in developed economies will fall far short of expectations.
But it is also hoping to regain some authority over the markets, which increasingly seem to doubt the cartel's ability to influence prices.
Over the past few years, Opec quota alterations have had little effect, while non-Opec countries such as Russia, Norway and Mexico have ramped up production to profit from a surge in prices since 1999.
Opec claims that this production has caused a glut in the market.
"There is an oversupply of 1.3-1.5 million barrels per day and so that is the amount that needs to be cut between Opec and non-Opec," Venezuelan Oil Minister Alvaro Silva said ahead of the Opec meeting.
But the global economic slowdown - which has reduced demand for fuel around the world - has also played a significant role in the oversupply.
Opec problems
Other Opec members such as Nigeria, Algeria and Indonesia are having their own economic problems, so are extremely reluctant to cut output in the uncertain hope that they may be compensated by higher prices.
The difficulty has sparked wild speculation about new pressure tactics, including rumours of a planned price war led by Saudi Arabia and Kuwait.
In 1986, the two countries produced at full throttle, driving down prices and forcing non-Opec producers to come to heel.