The next five weeks are shaping up to be one of the most crucial periods yet for the Organization of Petroleum Exporting Countries as it plots a production response to the recent rapid rise in oil prices.

Officials of the 13-member cartel are scheduled to meet June 5 in Vienna to set production and quota levels for the second half of 1989.

How OPEC resolves these issues, amid mixed opinions on the outlook for oil demand, will determine whether oil prices rise or retreat, and by how much and for how long.

The Exxon Valdez disaster in Alaska and the disruption of 25 percent of Britain's North Sea oil production for at least four weeks because of an explosion pushed the U.S. futures price of West Texas Intermediate (WTI) crude to its highest level in more than three years, although the price later fell back.

Meanwhile, higher-than-expected demand for gasoline so far this year has allowed OPEC to consistently pump more than its current ceiling of 18.5 million barrels of oil a day without undermining the oil price rally that began last November.

Now, several producing countries are gearing up to raise output.

But the cartel faces trouble. It is "virtually impossible to fine-tune output to short-term market conditions, especially when prices do not act as a good barometer of the prevailing fundamentals," the Washington-based Petro Finance Market Intelligence Service said in its latest newsletter.

The consensus in the industry is that a looming surge in OPEC production combined with a seasonal decline in demand during the second quarter could create a potential glut of up to 3 million barrels a day and force oil prices down by about $3 a barrel to the $18 range.