When they agreed to the new production cuts in December, the so-called OPEC+ alliance said it would assess the oil market in April, two months ahead of OPEC's usual meeting in June. But on Monday, a committee tasked with monitoring the deal said "market fundamentals are unlikely to materially change in the next two months."
The Joint Ministerial Monitoring Committee said it will next meet in May, with the full group convening on June 25 to decide whether to extend the output cuts through the end of 2019.
The latest round of cuts have helped boost oil prices from 18-month lows this year. U.S. West Texas Intermediate crude has rallied 29 percent to more than $58 a barrel, while international benchmark Brent crude is up 25 percent to about $67 a barrel.
OPEC and its allies are aiming to keep 1.2 million barrels per day off the market, but some producers are still pumping above their quotas, including Russia, the world's second biggest oil producer.
Russian Energy Minister Alexander Novak told CNBC on Sunday that Russia will hit its target in coming weeks. He said it is premature to to discuss whether the group should continue capping output beyond June.
Falih said Monday he does not expect OPEC to leave the oil market "unguided in the second half," Dow Jones reported. Last month, the Saudi oil minister told CNBC he was leaning toward extending the production cuts through the end of the year.
Helima Croft, global head of commodity strategy at RBC Capital Markets, says the group is likely to continue cutting production throughout 2019. However, extending the cuts will highlight divisions between Russia, where partly private companies produce oil, and OPEC members like Saudi Arabia, where state-owned energy companies underwrite the nation's budget.
"The Russian corporates hate shutting in production. They benefit from volume. The state takes the upside of higher prices, so for them, they don't like the agreement," she told CNBC's "Worldwide Exchange" on Monday.
"But for Saudi Arabia and for the rest of the OPEC producers, current prices still remain below their fiscal breakevens, so they would like to see prices a bit higher from here."