The 11-nation group's members will meet at a conference on 22 May, and many observers hope for a decision then.
But while Opec members warned that an increase may not bring down prices, the EU said there was now an "urgent need" for more supply.
US light crude ended the day up 96 cents to $41.50, just 5 cents below Monday's historic 23-year high.
The call for Opec to increase production was led by EU commissioner Loyola de Palacio.
She said the global economy would bear "a very heavy cost" unless prices moderated.
A willingness to raise production - a suggestion made by Saudi Arabia and backed by the United Arab Emirates - was, she warned, "a question of credibility for Opec".
"The problem today is not a crude oil problem. It is a gasoline market problem"
"If it does not come about, we will clearly see that Opec is not interested in oil price stability," de Palacio said.
But Opec members are already pumping 85-95% of capacity, according to the cartel's Indonesian president Purnomo Yusgiantoro.
"The problem today is not a crude oil problem," he said. "It is a gasoline market problem."
Demand is being boosted by a number of factors, including the uncertainty in Iraq, vast demand from the fast-growing Chinese economy and low stocks in countries across the developed world who are choosing to stockpile because of tensions in the Middle East.
Opec's most recent figures show that its 10 members who are meant to cap production are already quota-busting to the tune of 2.1 million barrels a day above the 23.5 million target.
With that kind of over-production, experts say, only Saudi Arabia and the UAE have much headroom to pump more.
For other members, a quota rise would only legitimise their existing output.