US benchmark West Texas Intermediate was up about five percent at $23.94 a barrel in Asian afternoon trade, after earlier rallying almost eight percent.
Brent crude, the international benchmark, also fell slightly from an earlier strong rally to trade 4.2 percent higher at $32.83 a barrel.
While the rises were healthy, they were limited compared to the double-digit jumps and falls of recent weeks, with analysts concerned there will be still be massive oversupply in the market as the virus pandemic throttles demand.
OPEC producers dominated by Saudi Arabia and allies led by Russia thrashed out a compromise deal Sunday after Mexico had balked at an earlier agreement struck on Friday.
The videoconference summit agreed to a cut of 9.7 million barrels per day from May, according to Mexican Energy Minister Rocio Nahle, down slightly from 10 million barrel reduction envisioned earlier.
OPEC Secretary General Mohammad Barkindo called the cuts “historic” — and the agreement appeared to mark an end to a bitter price war between Riyadh and Moscow.
Oil markets have been in turmoil for weeks as lockdowns and travel restrictions imposed to combat the outbreak batter demand, while the Saudi-Russian row compounded the crisis.
But analysts were left disappointed at a cut that will go nowhere near to making up for the expected demand loss due to the pandemic, forecast at anywhere between 15 and 30 million barrels a day.
Storage tanks worldwide are also rapidly filling up.
“The deal is a little less than the market expected,” Andy Lipow, president of Lipow Oil Associates LLC in Houston, told Bloomberg News.
“The hard work lies ahead given that the market is very sceptical that OPEC+ are actually going to be able to come up with their near 10 million barrels a day of production cuts.”
AxiCorp’s Stephen Innes added: “There remain concerns the agreement could be a day late and a ‘barrel short’ to prevent a decline in prices in the coming weeks as storage capacity brims”.