Hyundai said its chairman Chung Mong-Koo and his son would set aside assets worth one trillion won (£560m).
"We bow to the people and apologise," the firm said in a statement.
Prosecutors are investigating claims that Hyundai operated a multi-million dollar slush fund to bribe government officials to smooth the passage of Hyundai’s control over Kia.
"The Hyndai Motor Group, which should have set an example for society, failed to meet its social obligations and caused concern to the people," the firm said.
"The Hyundai Motor staff humbly accept the reproaches from the people. We will faithfully carry out our social obligations, keep to ethical standards and establish a transparent management system."