After years of doing too little, OPEC could suddenly be doing too much.

The Organization of the Petroleum Exporting Countries’ 14 members and other major producers like Russia are widely expected to strike an agreement this week to continue withholding about 2% of global oil supply from the market. The national energy ministers of about two dozen countries are set to meet Thursday at the oil cartel’s headquarters in Vienna.

But OPEC is beset by doubts that renewing its production agreement for another several months will help its members, say OPEC representatives and independent market watchers. Some members, along with outside analysts, say that OPEC could overstimulate the market and send prices too high next year. That, in turn, risks depressing demand for crude.

“There’s actually a chance the market will over-tighten and prices go close to $70 soon,” said Doug King, chief investment officer of the Merchant Commodity hedge fund, which has $165 million under management. “But they are also vulnerable if they don’t extend, that will spook the market.”

Brent crude, the international benchmark, is already up more than a fifth in the past three months, closing at 63.86 a barrel on Friday. U.S. crude oil futures settled 1.6% higher at $58.95, the highest closing level since June 2015. The upward trend is partly thanks to OPEC’s production limits but also to geopolitical threats to production in Iran, Iraq and Saudi Arabia, and Saudi public statements suggesting the kingdom is committed to supporting oil prices.

For years, OPEC had fought against a perception that it was no longer relevant to an oil market shaped by U.S. shale drillers. The cartel did nothing when oil prices crashed in 2014. Then, when it finally decided to cut production last year, the desired effect—higher prices—took longer than expected.

Today, investors and executives worry the cartel is overdoing it.

“I’m used to OPEC not doing enough,” said Rainer Seele, chief executive of oil company OMV AG. “Now they are over-delivering.”

Overshooting their mark could hurt demand for crude around the globe and accelerate a push toward electric vehicles and other technologies expected to cut into oil consumption.

Higher prices could also incentivize U.S. shale producers to ramp up drilling, raising the prospect of a flood of new oil that could depress the market. American producers seem already to be taking advantage. After falling for much of the past three months, the number of rigs drilling for oil rose by nine to a total of 747 this past week , according to oil-services company Baker Hughes.

Saudi Arabia, OPEC’s most powerful member, has advocated for extending the production cuts for another nine months, through the end of 2018. The kingdom needs higher prices as it plans an initial public offering of the state-owned Saudi Aramco, the world’s biggest oil-producing company. The IPO is the centerpiece of a plan to transform the kingdom’s economy, lessening its dependence on oil and developing the world’s largest sovereign-wealth fund to create new industries.

But Saudi oil officials say they also don’t want to overdo it. Saudi energy minister Khalid al-Falih told Bloomberg TV this month that the kingdom doesn’t want “any spikes in prices that shock the market, we don’t want any price movements that are not healthy for demand.”

“Our preference is that the market balances gradually,” Mr. Falih said.

Crude's Rise

OPEC strategy and geopolitical threats to production in Iran, Iraq and Saudi Arabia are driving Brentcrude-oil futures prices higher.

Not all OPEC members think the extension is a good idea. Most are reeling economically and politically from oil prices that are still around half of their 2014 levels. Higher prices would also lead to members cheating on their production targets to sell more crude, analysts say.

Ecuador, for instance, has already all but said it won’t comply with OPEC directives. OPEC members like Libya and Nigeria, which aren’t bound to production limits because of civil strife, have also posed problems for the cartel, as their production rises.

“I’m not sure all of us wanted to be in that deal for that long,” said an OPEC delegate from a Persian Gulf country where there are lingering doubts about the efficacy of the production cuts that the cartel and 10 other nations agreed to implement this year.

There are signs the production cuts have helped drain the global glut of oil. Industry stocks in the Organization for Economic Cooperation and Development, a group of some of the biggest developed countries, fell by 40 million barrels in September, to below 3 billion barrels for the first time in two years, according to the International Energy Agency.

Oil-market investors have called on OPEC to create a so-called exit strategy —a plan for eventually increasing production that doesn’t tank the market.

OPEC’s task is “about managing expectations,” said UBS oil analyst Giovanni Staunovo.

By Georgi Kantchev and  Summer Said