Both countries have been rebuked by the court, with Kenya accused of allowing intimidation of witnesses in an ICC case against its deputy president and South Africa under fire for not extraditing Sudan`s leader when he was in the country in June.
Set up in 2002 to try the most serious international crimes, the ICC has been criticized for only bringing charges in Africa, leading many on the continent to portray it as a largely European-funded neo-colonial institution.
The tensions risk driving a wedge between Europe and Africa at a time when Europe is seeking allies in the Middle East and North Africa in its fight against Islamist militancy.
Kenyan Foreign Minister Amina Mohamed said African countries had been "humiliated" by the court when an African Union summit in Johannesburg was overshadowed by the row over South Africa`s failure to arrest Sudan`s President Omar al-Bashir.
"All of us felt totally humiliated in June in Johannesburg," she said. "We weren`t allowed to focus on the issues that were important to the continent - peace, security, Burundi, Somalia, Mali. Totally distracted by this `arrest the president` movement."
"We want to be (ICC) members," she added. "When people leave a relationship they don`t leave for frivolous reasons. They leave if there is no space to move around... The space (for us) has shrunk."
Kenyan Deputy President William Ruto is on trial at the ICC for crimes against humanity, in connection with a wave of violence after the 2007 presidential election in which 1,200 people were killed. The case against President Uhuru Kenyatta, who faced similar charges, collapsed because witnesses were intimidated into withdrawing their testimony, judges said.
With Ruto, prosecutors want to continue the trial using statements witnesses gave before they withdrew. Kenya wants the court`s general assembly, meeting in The Hague this week, to declare that illegal.
The court has warned members against compromising its integrity by interfering in judicial decisions.
Sudan`s Bashir, who was allowed to leave South Africa rather than face arrest during the AU summit, is charged with genocide in relation to massacres in the western region of Darfur.
"Hosting the summit ... we had obligations in relation to the customary law insulating heads of state (from arrest)," said South African Justice Minister Michael Masutha.
A deputy government minister said last month that the ICC had "lost its direction" and the ruling African National Congress wanted to withdraw from membership of the court.
International court urged to reform or risk losing Africa
20 November 2015
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The International Criminal Court faced calls to change its approach in Africa or face losing some of its largest members as Kenya and South Africa joined forces at its general assembly to lobby for more freedom to interpret the court`s rules.
