Delegates from more than 100 nations, the tribunal's top officials as well as rights and lawyers are in Kampala for a two-week meeting aimed at reviewing the court's performance so far and widening its powers.
"Few would have believed then that this court would spring so vigorously into life, fully operational, investigating and prosecuting war crimes and crimes against humanity," Ban told the delegates.
"In this new age of accountability, those who commit the worst of human crimes will be held responsible."
The meeting in the Ugandan capital brings the court's top officials to Africa, which has produced all five of the cases currently under investigation by the war crimes prosecutor.
That reality has created tensions with some African leaders, who have charged that the Hague-based tribunal was targeting the continent in particular.
"Most of these situations were referred to the prosecutor by the governments themselves. Correctly, they see the court as a help to them, not a threat to them," Ban said.
"The court is meant to follow the evidence," he added. "The evidence will take the court beyond Africa sooner rather than later."
One of the most contentious issues to be discussed at the conference in Kampala will be extension of the court's powers to the crime of aggression.
While member states have informally agreed on how aggression should be defined, the real challenge lies in determining who has the power to initiate an investigation.
States have reportedly agreed that the United Nations Security Council should have the first say but rights groups argue the body should not have final authority.
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