But experts warned that the gains from the Riyadh agreement could be overwhelmed in the longer term as the Asian economic crisis and other factors cut demand and pushed down crude prices.
Yesterday the price of Brent blend rose by $2 per barrel on Friday's close to reach $14.18 (pounds 8.60) for spot crude and $15.18 for May delivery.
Oil companies have seen their shares hammered in recent months following down an oil price which had fallen from $25 per barrel a year ago to below $13 per barrel.
The stock market reacted positively yesterday, with BP shares rising 7.5 per cent to 933.5p, Shell Transport & Trading up 18.75p to 453p and Enterprise Oil up 30p to 573p.
The stock market bounce back followed a verbal agreement between Saudi Arabia, Venezuela and Mexico to curb output collectively by nearly 1 million barrels.
The oil market had been in freefall since November last year when Saudi Arabia and other OPEC countries decided to increase their production levels by 10 per cent.
These moves were almost immediately undermined by the currency crisis in south-east Asia, the UN oil export deal with Iraq and a warmer than expected winter. These made the supply/demand significantly crude prices to a 25-year low.
The agreement hammered out in Riyadh comes into effect on 1 April and runs until the end of the year. Saudi Arabia, Venezuela and Mexico have all agreed to cut their production by 300,000 barrels a day.
The three nations are hoping that other major producers will follow their lead so that 2 million barrels can be cut. Kuwait and Algeria have agreed to reduce their supplies by 125,000 and 50,000 barrels respectively but Egypt and Malaysia have refused.
The new agreement between Saudi Arabia and Venezuela from OPEC and Mexico, a non-OPEC supplier, was extremely important, according to the Oxford Institute for Energy Studies.
"It could be a watershed because it shows Saudi is willing to act without warning. Who will bet on $10 oil prices when producers are willing to bite back?" asked Dr Paul Horsnell, OIES deputy director .
It was also impressive because it brought together two previous antagonists in Saudi and Venezuela and not least because Mexico brokered the rapprochement.
Not since 1986 have OPEC and independent producers worked together to rein in supply. There are hopes that other non-OPEC members such as Norway might follow suit.
Fergus McLeod, oil analyst with NatWest Securities, said producers would not obtain the 2 million of cuts they want but half this figure will be enough to significantly affect prices.
Outlook, page 25