The “cabinet decided to hand over wanted officials to the ICC,” state media quoted Mariam al-Mahdi as saying.
The minister did not give a time frame.
Mahdi announced the decision during a meeting with visiting ICC chief prosecutor Karim Khan on Tuesday, according to state news agency SUNA.
The ICC issued arrest warrants for Bashir in 2009 and 2010.
The 77-year-old former president, who is held in Khartoum’s high-security Kober prison, is wanted by the ICC for alleged genocide, war crimes and crimes against humanity perpetrated in Darfur over a decade ago.
Conflict broke out in Darfur in 2003 after mostly non-Arab rebels rose against Khartoum. To date, up to 300,000 people have been killed and 2.5 million displaced, including more than 180,000 in West Darfur, according to UN estimates.
Last week, Sudan’s cabinet approved a draft bill to join the ICC’s founding Rome Statute.
The foreign minister noted that the bill and the handover of the wanted officials would be discussed for final approval during a meeting between the cabinet and the ruling sovereign council.
Sudan’s governing council, which is comprised of civilian and military leaders, was founded in August 2019 after the military overthrew Bashir in the wake of mass protests against his rule.
The council, Sudan’s highest executive authority, is tasked with leading the country to free and fair multiparty elections.
In December 2019, Bashir was sentenced to two years of detention in Sudan for corruption.
Since July 2020, he has been on trial in Khartoum for the 1989 coup which brought him to power. He faces the death penalty if convicted.
Violence continues in Darfur, about a year after Khartoum and key Darfuri rebel groups signed a peace deal.