Taous Feroukhi, chairwoman of the the IAEA's board, said the meeting was "an opportunity for the five candidates to address the entire membership" of the agency.
"It will help the member states have an objective assessment of the five candidates. This is the main purpose," she said, adding that there would be no formal vote on the day.
Jean-Pol Poncelet from Belgium, Yukiya Amano of Japan, Ernest Petric of Slovenia, Abdul Samad Minty of South Africa and Luis Echavarri of Spain each gave a short presentation to the board.
|Luis Echavarri, left, and Abdul Minty appeared before the IAEA board in Vienna [AFP]
After the meeting Amano, 62, said: "Everyone is strong. Everyone is a serious candidate. All of us have different background and different experience.
"This is a very transparent and competitive process. I think this is good for strengthening agency."
Echavarri, the Spanish candidate, said it was fundamental for the agency to remain independent and objective.
"I think as a director-general you have to be very well aware of the political consequences of what you do," he said.
ElBaradei's successor will take over sensitive investigations into the nuclear activities of Syria, Iran and North Korea, and will also have to persuade member countries to contribute more money to the agency's budget.
Speaking to Al Jazeera, Andreas Persbo, a nuclear arms control expert, said: "The agency faces many challenges in the coming years.
"We have the entire issue with Iran that still needs to be resolved and the agency plays an important role here ... so you need a diplomatic, strong leader.
"North Korea ... are no longer members of the IAEA so he [the director-general] has no formal authority even to talk to them.
"North Korea has no intention of rejoining [the IAEA] and ... once called the agency the cat's paw of the United States, that just ran Western interests completely.
IAEA governors have been searching in vain for a strong consensus candidate who could bridge a damaging split between industrialised and developing nations.
Developed states are mainly concerned about nuclear proliferation while developing countries want someone who plays an active role in delivering nuclear technology around the world.
In March, a race between Amano and Minty was inconclusive after neither candidate was able to secure the two-thirds majority needed to become the agency's new chief.
Slovenia's candidate is a former a former IAEA ambassador, while Spain's Echavarri currently heads the Organisation for Economic Co-operation and Development's nuclear energy agency.
Poncelet is a former Belgian deputy prime minister, defence and energy minister, and current senior vice president of Areva, a French company which mainly specialises in nuclear power.
Persbo said: "I would say Echavarri stands out. He is a skilled diplomat, he has many years experience of dealing with nuclear issues.
"He is well liked in the Western group and he has a certain appeal also to developing nations."