Sanford admitted the affair at a tearful, rambling news conference Wednesday and said he had visited the woman, a longtime friend, three times. His admission came after lawmakers and reporters questioned where he had been for five days.
His staff said he was hiking the Appalachian Trail, but he was really on another trip to Argentina to visit his mistress.
His spokesman, Joel Sawyer, initially said he was unaware of any state funds being used for the governor's liaisons, but Sanford said Thursday in an e-mail statement that he will reimburse taxpayers for the economic development trip last June.
"While the purpose of this trip was an entirely professional and appropriate business development trip, I made a mistake while I was there in meeting with the woman who I was unfaithful to my wife with," he said. "That has raised some very legitimate concerns and questions, and as such I am going to reimburse the state for the full cost of the Argentina leg of this trip."
Sawyer said he did not know who paid for the other two trips.
Taxpayers paid $12,000 for a nine-day trip to Brazil and Argentina last year that ended in Buenos Aires on June 27.
That includes $8,687 for Sanford's plane ticket, and $453 in lodging. Project manager Ford Graham's ticket was $1,910.
The Republican governor's statement did not say how much he will pay back.
Sanford and state Commerce Secretary Joe Taylor arrived in Sao Paulo, Brazil, on June 21 of last year, according to an itinerary provided by Commerce officials. The delegation toured the area and attended briefings on ethanol, politics and the sugarcane industry.
On his fourth day in Sao Paulo, Sanford left for Cordoba, Argentina, where he went out with a hunting party in the early morning and had "personal time" for the rest of the day.
The trade delegation did not go to Argentina with him, but he was accompanied by a project manager from the Department of Commerce, "standard practice for meetings with public officials and prospective companies," said Kara Borie, department spokeswoman.
The next day, Sanford left for Buenos Aires, where Graham met him at the airport. The schedule included meetings with U.S. Embassy officials and "dinner on your own."
In an e-mail to his mistress a few days after he returned, Sanford reflected on their time together.
"Know that I miss you," Sanford wrote, according to e-mails obtained by The State newspaper in Columbia. His office has declined to confirm the authenticity of the e-mails. "Unbeleivably (sic) hard to imagine it has been a week. ... Want to write an indepth note with some thoughts on our visit when I know you are getting these emails. Hugs and much love. M."
Several top state Republicans are calling for answers. On Thursday, GOP Sen. Glenn McConnell, the state's top senator, said Sanford needed to answer questions about whether taxpayer money was used during the affair, but stopped short of calling for an investigation.
There are no indications the woman ever flew on the state plane or took trips to South Carolina paid for by taxpayer money.
Over the past year, Sanford is listed as a passenger on several dozen flights arranged by the state Department of Commerce, many of them with other state officials or his family members but no passengers listed as "confidential."
Sanford also had two taxpayer-funded trips to Argentina during his three terms in the U.S. House.