Delegates from 36 countries and 22 oil companies attended the meeting, called to discuss the global oil price crisis which has led to protests around the world.
Speculators and taxes blamed
"There are several factors behind the unjustified, swift rise in oil prices," Abdullah said, blaming speculators and rising taxes.
"In this critical hour, the world community should rise to its responsibility and co-operation should be the cornerstone of any efforts."
He said his country would step up production by 200,000 barrels to 9.65 million barrels a day from July in order to help ease the situation, but few other countries came forward with concrete plans to increase supply.
Al Jazeera's Amr El Kahky, reporting from Jeddah, said: "There was an optimistic atmosphere, but the much-anticipated Jeddah Energy meeting failed to meet expectations, providing little in the way of big solutions for global fuel crisis.
"They agreed to meet again in the next few months and seek to curb the effects of market speculation on oil prices, as well as to satisfy growing calls for transparent information regarding supply and demand."
There is no consensus on the cause of high oil prices.
The US and other Western countries have put increasing pressure on Saudi Arabia to increase production, saying insufficient oil production has not kept pace with growing demand.
Samuel Bodman, the US energy secretary, insisted before the summit that "there is no evidence that we can find that speculators are driving futures prices" to current record heights.
"In this critical hour, the world community should rise to its responsibility and co-operation should be the cornerstone of any efforts"
"Market fundamentals show that production has not kept pace with growing demand for oil, resulting in increasing ... and increasingly volatile prices," he said.
"Even despite higher global production for oil so far this year, inventories have been drawn down and current world production capacity is below historic levels - at fewer than two million barrels per day."
Cautioning that prices would almost certainly rise further, Bodman said: "In the absence of any additional crude supply, for every one per cent increase in demand we would expect a 20 per cent increase in price in order to balance the market."
However, Saudi Arabia and other Opec (Organisation of the Petroleum Exporting Countries) members say market demand is being met.
"I am convinced that the supply and demand balances and crude oil production levels are not the primary drivers of the current market situation and that markets are already well-supplied," Ali al-Naimi, Saudi's oil minister, said in a speech.
"A simplistic focus on supply expansion is therefore unlikely to tame the current price behaviour."
Mohammed al-Olaim, Kuwait's oil minister, said that Opec members "will not hesitate" to increase production if the market needs it.
Chakib Khelil, the president of Opec, said that oil cartel had decided no special meeting on production was needed now and that a decision would be made at the groups' regular meeting in September.
"We believe speculation, in its noble and not noble terms, has its impact," he said.
Khelil said much of the rising costs can be explained by currency-market turbulence.
"A lot of people are talking about the uncertainties about the reserves. But what about the uncertainties on the dollar?" he said.