* OPEC reacts to weak economy
* Softening of relationship with U.S.
* OPEC needs economic recovery to drive oil demand
By Barbara Lewis
VIENNA, March 16 (Reuters) - OPEC's decision on Sunday to resist new supply cuts laid the ground not just for cheaper oil to help heal the economy, but for warmer relations with the world's biggest energy consumer.
Two days after U.S. President Barack Obama called Saudi King Abdullah, OPEC said it would stick to existing supply targets, even though fuel inventories have swollen and oil prices are much lower than it would like.
The Organization of the Petroleum Exporting Countries said the weakness of the world economy, which effectively receives a financial stimulus from cheaper oil, was a central motivation.
It also gave a tentative welcome to the new U.S. administration.
"I don't want to say that I voted for Obama, but we can see a different tone ... that we didn't see in the past," OPEC Secretary General Abdullah al-Badri told reporters.
"We have seen a positive approach. They are ready for dialogue and we are ready for dialogue and ready for talk."
U.S. Energy Secretary Steven Chu said he was pleased with OPEC's latest output decision, although he restated the U.S. commitment to ending its dependence on foreign oil.
For OPEC, as for the rest of the world, the real issue was the economy, analysts said. Sheer self-interest dictated the group needed to avoid the kind of damage to growth that would only further limit energy consumption.
"At the moment, getting the world back on its feet is more important than lifting the oil price by a further $10 a barrel," said Lawrence Eagles of JP Morgan in New York.
"The world economy is crucial. Short-term gain would be to the long-term detriment of OPEC."
But analysts also said any gentle pressure from Obama, as opposed to from former president George W. Bush, might have been less disruptive to the producer group's debate, making consensus easier to achieve.
As well as U.S. ally Saudi Arabia, OPEC's members include established U.S. adversaries Venezuela and Iran, who went along quietly with Sunday's OPEC decision.
G20 MEETING
Sunday's talks against the backdrop of oil prices around $45 a barrel and shrinking demand as the weak world economy saps energy consumption stood in marked contrast to a meeting in Vienna almost exactly a year ago.
Before the meeting in March 2008, Washington had said even a modest output increase would help to calm oil markets, but OPEC instead kept supplies steady. In response, prices leapt to what was then a new record above $100 a barrel.
Rejecting the U.S. request, then OPEC President Chakib Khelil of Algeria shot back that the United States' mismanagement of the economy, not OPEC, was to blame for high oil prices.
Now the consequences of economic mismanagement are so much clearer, observers had predicted well before Sunday's meeting that OPEC would hesitate to deepen record output cuts, which have totalled 4.2 million barrels per day (bpd) since September last year.
Some said the Group of 20 summit of developed and emerging nations in April, to which Saudi Arabia is invited, was a major consideration and that could have been part of the telephone discussion between Obama and King Abdullah on Friday.
"They would not wish to appear to be undermining this meeting, which will focus on seeking resolutions to the global financial crisis," Sadad al-Husseini, a former top official at state oil giant Saudi Aramco, said last week.
OPEC's final communique on Sunday voiced the "hope that the decisions taken by the forthcoming meeting of G20 in April 2009 may contribute a substantial improvement to the world economy".
Its prime interest in the economy relates to its implications for oil demand, which is expected to drop by about one million bpd this year compared with last year.
OPEC has argued that for long-term economic health, oil prices need to be high enough to sustain investment in new production, but in the nearer term, it is resigned to allowing a weaker oil market.
"OPEC in general and Saudi in particular have been very vocal for some time on about the need to pay attention to the wider macro economic conditions," said David Kirsch, director of market intelligence services at PFC Energy in Washington.
"They would much prefer to have $50 or $60 or $75 oil, but they recognise that just isn't sustainable in the current economic environment and will have to live with prices in the band that they've been trading in for a some time to come, say the next two quarters."
(Additional reporting by Simon Webb; editing by William Hardy)