OPEC and its allies agreed to a small increase in oil production on Wednesday following calls by the U.S. and other major consumers for more supply, but the symbolic move is expected to have a minimal impact on crude prices.

The Saudi-led Organization of the Petroleum Exporting Countries was under some pressure after President Biden said he expected Riyadh to help boost global supplies following a high-profile trip to the kingdom last month. But OPEC needs to coordinate its production plan with a coalition of Russia-led producers with which it has an enduring alliance. Moscow prefers high prices.

In their sixth meeting since Russia invaded Ukraine in late February, sending oil prices above $100 a barrel for the first time in eight years, members of the broader alliance, called OPEC+, agreed to raise their collective production by 100,000 barrels a day in September, delegates said.

The alliance in June had agreed to boost output by 648,000 barrels a day in July and in August. Before that, OPEC+ rolled out monthly increases of 432,000 barrels a day as part of a plan to raise output to prepandemic levels. That deal ends in August, although many members are producing below their allotted quotas.

Meanwhile, oil prices, which soared as Covid-19 lockdowns eased and economic activity picked back up, have slipped in recent weeks on worries about global growth. The drop has erased most of the gains after Russia’s invasion.

In Wednesday afternoon trading in London, Brent crude, the international benchmark, was up 0.7% at $101.21 a barrel, while U.S. crude was 0.9% higher at $95.30.

The U.S. and other major oil-consuming Western nations have called on the alliance, which accounts for about half the world’s oil production, to pump more crude to help bring prices down. Russia prefers higher prices to make up for lost exports due to Ukraine-related sanctions.

OPEC delegates say the alliance needs more time to assess a possible slowdown in global energy demand before taking a call on boosting oil production by a significant amount. Saudi officials have sought to temper expectations, reiterating that the kingdom would do what is needed to balance the market if there is a shortage of supply.

Even then, the alliance’s ability to boost output remains limited. OPEC+ pumped nearly 3 million barrels a day less than its collective production target of about 42 million barrels a day in May, according to an independent assessment report commissioned by OPEC. The shortfall was due mainly to falling production in sanctions-hit Russia and chronic output problems in Nigeria, Angola and some other countries, according to OPEC delegates.

Meanwhile, Saudi Arabia, the member with the biggest spare capacity, is nearing its pumping limit. The kingdom is currently producing about 10.5 million barrels a day, according to people familiar with its oil operations. They say Riyadh would struggle to produce 11 million barrels a day for more than a few months at a stretch and 12 million barrels a day for more than a few weeks.

Overall, spare capacity is set to almost halve to 1.7 million barrels a day next year, another report commissioned by OPEC says. It will shrink to as little as 400,000 barrels a day in 2024 as producers respond to rising oil demand, it says.

“Retaining spare capacity to ensure the market has headroom is prudent especially as an energy supercycle takes hold over the coming years,” said Christyan Malek, head of oil-and-gas research at JPMorgan.

OPEC also expects global oil-demand growth to slow to 2.7 million barrels a day next year, from 3.4 million barrels a day in 2022. The cartel expects global growth to ease to 3.2% in 2023 from 3.5% this year as economies in Europe and the U.S. suffer from soaring inflation and interest-rate rises. Last month, the International Energy Agency, which advises energy consumers, cut its forecasts for oil demand this year by 240,000 barrels a day.

Write to Summer Said at summer.said@wsj.com and Benoit Faucon at benoit.faucon@wsj.com