ICC lawyer Fatou Bensouda said during a United Nations Security Council videoconference that Kushayb - who is suspected of crimes against humanity in Darfur - "was transferred to the court following his surrender" in the Central African Republic.
Bensouda congratulated Chad, France, the Netherlands and the UN mission in the Central African Republic but did not offer any other details about Kushayb's arrest.
"There should be no escape from justice for perpetrators of the world's most serious crimes under international law," she said, calling on others to surrender themselves.
"I take this opportunity to call Abdallah Banda and all the ICC suspects to surrender to the ICC and answer the charges against them through a fair, objective and independent judicial process."
Kushayb has been wanted by international law enforcement since 2007 for his role as head of the Janjaweed militia.
He is also a former close ally of ousted Sudanese president Omar al-Bashir, himself wanted by the ICC and currently detained in Khartoum.
Abdallah Banda has been wanted for war crimes since 2019 by the ICC, which is also searching for two other individuals related to the case.
Read also: Darfur war crimes fugitive in ICC custody
The Security Council members who helped found the ICC (Belgium, Dominican Republic, Estonia, France, Germany, Nigeria, St. Vincent and the Grenadines, South Africa, Tunisia and Britain) in a joint statement underlined their commitment to fighting against impunity from war crimes.
"We reiterate our commitment to uphold and defend the principles and values enshrined in the Rome Statute and to preserve its integrity undeterred by any threats against the Court, its officials and those cooperating with it," the statement said.
The United States is not a member of the ICC and Russia resigned from the group in 2016.
Follow us on Facebook, Twitter and Instagram to stay connected
Follow the Middle East's top stories in English at The New Arab on Google News
