OPEC Secretary General Mohammad Barkindo told an industry conference in London that January data showed conformity from participating OPEC nations with output curbs had been above 90 % and oil inventories would decline further this year.
"All countries involved remain resolute in the determination to achieve a higher level of conformity," Barkindo said.
Benchmark Brent crude oil jumped $1.13 a barrel to a high of $57.31 before easing to trade around $57.20 by 1410 GMT.
U.S. light crude was up $1.20 at $54.60, having risen by about 0.5 % in a shortened session on Monday because of a U.S. national holiday.
The Organization of the Petroleum Exporting Countries and other producers outside the group agreed in November to cut output by about 1.8 million barrels per day (bpd) in an effort to drain a glut that has depressed prices for over two years.
The cuts have spurred a speculative move into crude oil that has pushed prices towards the top of their recent ranges.
Money managers now hold the highest volume of net long Brent futures and options on record, InterContinental Exchange data showed on Monday, betting on higher prices to come as OPEC and other key exporters reduce production.
Net long U.S. crude futures and options positions are also at a record high, U.S. data showed on Friday.
"This prolonged and increasing overcrowding of speculative net longs should be a cause for concern," said Jonathan Chan, an investment analyst at Phillip Futures.
"Should there come a time when these speculative positions decide to unwind, oil prices will be in for a significant correction."
Despite signs that OPEC's agreement is holding, inventory levels are still very high in many parts of the world.
U.S. crude oil and gasoline inventories soared to record highs last week as refineries cut output and gasoline demand softened.
More evidence of the state of the U.S. oil market will come on Thursday when the U.S. Department of Energy publishes stocks figures. Those numbers could be a catalyst for a market move, said Carsten Fritsch, an analyst at Commerzbank in Frankfurt:
"Until then, lack of bearish news seems to be enough to push prices higher," Fritsch said.