* OPEC debates tighter compliance or more cuts
* High oil stocks and weak world economy overshadow talks
By Simon Webb and Alex Lawler
VIENNA, March 15 (Reuters) - OPEC ministers weighed the options of tighter compliance with existing output curbs or agreeing to new cuts as they prepared to meet on Sunday against a backdrop of high oil stocks and a damaged world economy.
Ministers from the 12-member Organization of the Petroleum Exporting Countries have said the first item on the agenda was tighter enforcement of agreements since September to lower supply targets by 4.2 million barrels per day (bpd).
But they have yet to rule out also agreeing deeper cuts to stave off further price weakness and pre-empt more rises in inventories as demand sinks.
"It could go either way," OPEC Secretary General Abdullah al-Badri told reporters on Sunday when asked which course of action ministers favoured.
Consumer nations have put pressure on the group to avoid pushing oil sharply higher, which they say could inflict further damage on a shattered world economy.
The International Energy Agency, which represents consumer countries, has said cheaper oil amounted to a trillion-dollar financial stimulus and Barack Obama, president of the world's biggest energy consumer the United States, called Saudi King Abdullah last week.
On arriving in Vienna on Saturday, Saudi Arabian Oil Minister Ali al-Naimi placed the emphasis on output discipline.
"Compliance is very good," Naimi told reporters. "We'd like to see compliance as high as possible. It is over 80 percent now, it can be better."
He said the output cuts were reducing oversupply, but demand was expected to stay weak as economic output shrank.
"You have to understand that the world economy is not as healthy as it should be. We should expect demand world-wide to be down," Naimi said.
ALGERIA SPEAKS OUT
Algerian Energy and Mines Minister Chakib Khelil has been the most forthright in stating further action was needed to take away oversupply.
Asked whether OPEC should cut or just comply with existing restrictions, Khelil replied: "Both ... comply and cut."
He said the oil market had already factored in another reduction of at least 500,000 bpd, with the implication prices would fall if that does not happen.
Whatever the outcome of Sunday's meeting, Saudi Arabia, the world's leading exporter and the best-placed to add or subtract barrels of oil, could decide unilaterally how much it thinks the market needs.
Independent observers have said the kingdom was already pumping less than its implied target.
OPEC's cuts since last September are the deepest and most rapid yet and the strong compliance has helped to pull prices up from a low of $32.40 in December to around $46 at close of trade on Friday.
OPEC can draw satisfaction from the price recovery, but levels are still just over $100 below last year's record high and the group cannot forget the price crash in the late 1990s when oil fell towards $10 a barrel.
Output cuts then were implemented more slowly than this time round and prices did not stabilise for more than a year.
A difference between then and now is that fuel demand was only flat. This time, the energy sector's leading forecasters have predicted it will decline by at least one million bpd in 2009 compared with 2008 and the world economy is far weaker.
Another difference is that non-OPEC supplies are falling because of under-investment and the maturity of many oilfields.
That means any cooperation from non-OPEC countries with OPEC output cuts would be largely academic.
Some OPEC ministers have nevertheless called on the leading non-OPEC producer Russia to join in.
Moscow has sent a high-level delegation, including Deputy Prime Minister Igor Sechin and Energy Minister Sergei Shmatko, to attend Sunday's meeting as an observer.
For related graphic, showing the relationship between OPEC output cuts and the oil price, please click on:
https://customers.reuters.com/d/graphics/OL_OPEV0309.gif (For a factbox on past OPEC production changes)
(Additional reporting by David Sheppard and Henrique Almeida, Writing by Barbara Lewis; editing by William Hardy)