Oil production group Opec is expected to leave its output quotas unchanged at a meeting later this week, despite pressure from some members for a cut.
Venezuela has said that supplies are strong enough to merit a cut
Analysts said that even though oil supplies have improved, Opec members do not want to be seen pushing prices up as they are near record levels already.
However, Venezuela has argued for a cut in the 28-million-barrel daily quota precisely because supplies are strong.
The 11 Opec member states will meet for talks in Caracas on Thursday.
Opec has held its output quota unchanged since the middle of last year to ease concerns about supply shortages that were fanned by concerns such as tensions between the US and Iran, and attacks on infrastructure.
"People are looking at Iran and waiting for the big Opec meeting," said Tetsu Emori of Mitsui Bussan Futures.
Opec members include Saudi Arabia, Iraq, Iran and Nigeria, and the cartel provides more than a third of the world's oil.
Figures have shown that Opec's output has consistently been more than 28 million barrels a day, and often close to 30 million a day.
But Venezuela's Oil Minister Rafael Ramirez said he would use Thursday's meeting to call for a cut to the quota of between 500,000 and 1 million barrels a day.
However, Mohamed al-Hamili, the oil minister from the United Arab Emirates said he expected quotas to stay where they are when Opec meets this week.
The group's President, Edmund Daukoru, said that Opec would "do the best we can within our capacities without formally announcing unrestricted production".
"Asking people to do more when they are already doing all they can doesn't make sense," said Mr Daukoru, who is also Nigeria's oil minister. "I don't think anyone is holding back spare capacity."
Analysts said that it would be risky to assume that all supply problems had passed, especially with demand for crude and petrol expected to increase in the US over the summer driving period and during the hurricane season.
These concerns kept oil close to the $71-a-barrel mark in New York and London on Tuesday.
"It would be a very bad signal to cut quotas at $70-$71 per barrel," said Frederic Lassere, an analyst at SG Securities.
"From a political point of view it would be very, very difficult to justify to the consumers."
A barrel of New York light crude was trading at $71.52, while London's Brent was at $70.73.