"The African Union (has) drawn our attention to the need for greater logistical support, particularly for transporting troops, particularly for housing troops, equipping troops," said EU aid commissioner Louis Michel.
"So, we have taken careful note," he told reporters.
The Darfur conflict, which pits rebels against pro-government militia, has resulted in the deaths of between 180,000 and 300,000 people and forced some two million others to flee their homes.
Last month, UN humanitarian affairs chief Jan Egeland said there was an urgent need to expand the AU's mission to prevent the number of displaced Darfur residents from rising to three or four million.
The fighting began in February 2003 after black African groups rebelled against what they see as persecution from Khartoum's Arab-led government.
The African Union hopes to have almost 8,000 troops in Darfur by the end of September but EU foreign policy chief Javier Solana sought to allay any concerns that Brussels would send troops.
"The soldiers will be African Union," he said after his own brief round of talks with Konare. "The only thing the European Union is going to do is provide planners, these will be in the tens, not in the thousands."
Konare insisted that the AU wants to be in full control of the mission and that it is only seeking logistical help and support of a more general manner.
Providing support has, indirectly, been a source of tension between the EU and NATO; more precisely, between France and the United States.
France is opposed to a NATO role in Sudan -- playing "the world's policeman" in the words of French Foreign Minister Michel Barnier -- and Solana and NATO chief Jaap de Hoop Scheffer were clearly aware of the problem.
"There will be a meeting later in month of all the contributors, the European Union and NATO, the member states ... meeting in Addis (Ababa, Ethiopia) to see how things can be done better," Solana said.
De Hoop Scheffer, for his part, said that the Alliance was looking into how it might be able to help Darfur in "full transparency with the European Union".
"I'm confident that NATO will be able to answer the call," he said, alluding potentially to what would effectively be the first Alliance mission in Africa.
"NATO does not have the ambition of being the world's policeman," he went on, and said it would be possible "to imagine a certain division of responsibilities."
"Who would do what, is a little early to say," de Hoop Scheffer added.