But Museveni has accused the ICC of what he calls "arrogance" in its handling of Kenya's post-election violence case.
"I was one of those that supported the ICC because I abhor impunity," he said in April in Nairobi, Kenya's capital. "However, the usual opinionated and arrogant actors using their careless analysis have distorted the purpose of that institution. They are now using it to install leaders of their choice in Africa and eliminate the ones they do not like."
Kenyatta and Ruto have both pledged to continue cooperating with the ICC, even though Kenya's parliament recently voted to withdraw from the ICC. Ruto's trial is under way and Kenyatta's is scheduled to start in November.
Thirty-four African countries, including Nigeria and South Africa, have signed the Rome Statute.
When an African Union summit in May urged the United Nations to transfer trials of Kenya's leaders to Kenya, Ethiopian Prime Minister Hailemariam Desalegn said the ICC prosecutions "have degenerated into some kind of race hunt" of Africans. "We object to that," he said.
Amnesty International said recently that Kenya's exit from the ICC would "set a dangerous precedent for the future of justice in Africa."
A mass exit of African countries from the ICC "would weaken its political and practical ability to seek justice for victims of atrocity," said David Crane, a law professor at Syracuse University in the U.S.
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Odula reported from Nairobi, Kenya.