Korean media reports have alleged that Choe Heung-sik, head of the Financial Supervisory Services (FSS) since September, in 2013 asked Hana Financial Group to illegally hire the son of a colleague.
In a statement on Monday, Choe denied any wrongdoing, saying that he was never involved in the bank's personnel decisions and did not conduct any "illegal acts".
"However, my actions at the time might not fit the current public sentiment", he said in the statement released by the FSS.
Choe's statement said it was his duty to step down "in order to ensure the impartiality of the FSS, which is investigating employment irregularities in the financial sector".
President Moon Jae-in has yet to accept or decline his offer of his resignation, an official at the Blue House said.
From 2012 until 2014, Choe was president of the Hana Financial Group, which owns KEB Hana Bank, South Korea's biggest lender.