Kang Un-tae has been accused of forging the signatures of former prime minister Kim Hwang-sik and former culture minister Choe Kwang-shik on a bid document that guaranteed public funding for the event.
Despite the allegations, world governing body FINA awarded Gwangju hosting rights for the 2019 event on Friday.
"I deeply apologise for a shameful thing," Kang told reporters on Monday. "Discovered by the Prime Minister's Office on April 29, I was informed by South Korea's bid committee secretary general as he briefed me on the matter.
"In the process of submitting a bid document to FINA by April 2, a mistake by an official led to the signatures on the government guarantee and contents to be altered."
Kang said he had apologised to the government, who were aware of the issue and subsequently promised to finance the organising budget during a meeting with FINA in May.
"I will successfully carry out the first ever (swimming) event hosted in Korea after I iron out conflict and mistrust with the government," Kang added.
"I will ask for cooperation through a meeting with the prime minister and the (culture) minister."
The Prime Minister's office, however, told Reuters that they had not promised any financial support to the organisers.
The government has also ordered a further investigation into the forgery allegations and promised strict actions against anyone found guilty.
Barcelona is hosting the ongoing world championships while Russia's Kazan will host the 2015 edition, followed by Guadalajara in Mexico two years later. The Hungarian capital Budapest was awarded hosting rights for the 2021 championships.
- Politics & Government