Brent crude ended Thursday 0.4% higher at $49.94 a barrel.
Prices initially fell but then reversed course when figures showed that US crude stockpiles had fallen in the past week.
In a statement, Opec said its members were committed to a "stable and balanced oil market".
Speaking after the meeting, Saudi Arabia pledged that it would not flood the market by increasing production.
The country's energy minister, Khalid Al-Falih, said: "We will be very gentle in our approach and make sure we don't shock the market in anyway."
Opec members produce 40% of the world's crude oil.
A meeting of most Opec members, along with other oil exporters including Russia, similarly failed to cap output following a meeting in Qatar in April.
John Hall, an oil analyst with alfaenergy, said: "Now that there is a realisation that Opec will not be restricting output, traders are caught long with too much oil in a falling market and so once $50 had been reached, there was a general mood to sell off rapidly."
After peaking at about $115 a barrel in the summer of 2014, the price of oil fell steadily to a low of about $27 in January this year due to a combination of weaker demand and increased supply.
Opec secretary-general Abdulla al-Badri denied that the failure to cap output meant that the cartel was dead: "Opec will be powerful, will be strong. Opec is alive."
Bob Minter, analyst at Aberdeen Asset Management Investment, said: "This should have been an easy meeting to re-establish Opec relevance, but they missed the opportunity."
The oil ministers did agree that Nigeria's Mohammed Sanusi Barkindo would become Opec's new secretary-general from 1 August.
The decision ended years of dispute between Saudi Arabia and Iran, which had put forward their own candidates and refused to agree on a compromise.
The ministers also agreed to admit Gabon as the 14th member of Opec from next month.
The price of oil rose slightly despite a meeting of the Opec oil producers' group failing to set a cap on the amount of oil the group produces.