A deferral of The Hague trial of Kenyan President Uhuru Kenyatta – due to start in November – has been demanded at the African Union summit in Ethiopia.
The AU also agreed a resolution stating no sitting African head of state should appear before an international court.
With both Kenyan and Sudanese presidents facing ICC cases, African leaders have long complained that the court unfairly targets them.
The AU had discussed withdrawing from the ICC, but failed to get support.
Senior figures including Kofi Annan have criticized plans to quit the ICC.
The AU leaders, meeting in Addis Ababa, agreed to back immunity for any sitting African head of state.
They also asked Kenya to write to the UN Security Council seeking a deferral in the International Criminal Court (ICC) case against Kenyan President Uhuru Kenyatta, who faces charges of crimes against humanity.
Both he and his deputy, William Ruto, deny charges of organizing violence after the 2007 election.
While William Ruto went on trial in September, President Kenyatta has repeatedly requested his trial – due next month – be postponed.
Addressing the summit, Uhuru Kenyatta accused the court of bias and “race-hunting”, AFP reports.
“The ICC has been reduced into a painfully farcical pantomime, a travesty that adds insult to the injury of victims. It stopped being the home of justice the day it became the toy of declining imperial powers.”
Ethiopian PM and AU chairman Hailemariam Dessalegn said the summit was not a crusade against the ICC but a call for the court to address Africa’s concerns seriously.
He said the ICC’s cases against the Sudanese and Kenyan presidents could hamper peace and reconciliation efforts in their countries.
“The unfair treatment that we have been subjected to by the ICC is completely unacceptable,” he said.
The ICC issued a warrant in 2009 for Sudanese President Omar al-Bashir over alleged war crimes in the Darfur region, but he has not yet been arrested.
The ICC relies on the authorities of national governments to hand over suspects, but Mr Bashir has avoided arrest despite travelling to countries that have signed up to the ICC statute.
Ethiopian Foreign Minister Tedros Adhanom Ghebreyesus, who is the current chairman of the AU’s Executive Council, said the ICC had failed to respond to the African Union’s previous complaints.
“What the summit decided is that President Kenyatta should not appear until the request we have made is actually answered,” he said.
Thirty-four of the AU’s 54 members have signed up to the ICC.
Kenya’s parliament has already passed a motion for the country to withdraw.
Former UN Secretary-General Kofi Annan has said that withdrawing from the court would be a “badge of shame”.
Nobel Peace laureate Archbishop Desmond Tutu has also voiced his support for the ICC.
“Those leaders seeking to skirt the court are effectively looking for a license to kill, maim and oppress their own people without consequence,” he wrote in an article carried by several newspapers.
“They simply vilify the institution as racist and unjust, as Hermann Goering and his fellow Nazi defendants vilified the Nuremberg tribunals following World War II.”
All eight of the cases currently open at the ICC are in Africa but it is also investigating possible cases elsewhere.