The Republican said in a statement Thursday that he visited with the woman during the trade mission to Brazil and Argentina last June. Sanford said he "made a mistake" in seeing the woman while in Argentina.
State Commerce Department records indicate more than $8,000 was spent in airfare, lodging and meals. The governor's statement does not say how much he will pay back.
Meanwhile, Sanford faced legal and ethical questions Thursday as he fought to save his job after admitting the extramarital affair.
The state's top senator questioned whether Sanford broke the law when he disappeared for several days on trip to South America and didn't transfer power to the lieutenant governor.
"I would think that if the evidence indicates that there is a willful effort to circumvent the constitution, I think there would be a chorus of calls for him to resign," said state Sen. Glenn McConnell, a fellow Republican.
McConnell said Sanford needed to answer questions about whether taxpayer money was used, but stopped short of calling for an investigation. Sanford's spokesman has said no state resources were used during the affair.
On Thursday, Sanford was with his family at their beach home on Sullivans Island, spokesman Joel Sawyer said. First lady Jenny Sanford and the couple's four sons have been staying at the house.
Sanford's wife Jenny was not with him when he admitted at a news conference Wednesday that he had been having an affair and was in Argentina during his unexplained absence. Both have said they plan to try to reconcile.
Jenny Sanford said late Thursday that her cheating husband can worry about his own career. She is concerning herself with their four sons.
She said she's taking things one day at a time and appeared upbeat and laughed when stopping to talk with media. She said she was taking her sons out to dinner and on a boat ride.
Sawyer says Sanford has spent the last two days touching base with other elected officials and has personally apologized to his staff.
Many critics say his worst political offense was leaving the state without a word, reports CBS News correspondent Kelly Cobiella. On the street many voters are furious.
"I think it's a disgrace," Carol Coddy told Cobiella. "I think he ought to be ashamed of himself. I think he's an embarrassment to our country."
"I don't think he really deserve the office," Melvin Belton said. "I pray for him, but I've lost confidence."
Sanford was a three-term U.S. House of Representatives veteran who once cited "moral legitimacy" when he was a congressman voting for President Bill Clinton's impeachment in the 1990s. As governor he's become a darling of fiscal conservatives over his ideological opposition to federal stimulus cash.
Now Sanford has taken a swan dive from the moral high ground.
By admitting to an extramarital affair, the Republican governor makes the already-difficult end of his term-limited administration nearly untenable.
He has alienated leaders of his Republican-dominated state Legislature for years, but said recently he was finding comfort outside the Statehouse as a champion for smaller government and lower taxes.
He was raising his national political profile with his outspoken fight against using federal cash for anything but paying down debt. As chairman of the Republican Governors Association, he was raising money for candidates and deflecting talk he was planning to run for president in 2012.
The speed of his collapse was shocking. Even his former chief of staff and friend of 30 years, state Sen. Tom Davis, said he didn't know about the affair until Wednesday.
"I think that South Carolinians, in particular Americans, have tremendous capacity for forgiveness. That said, they can also recognize hypocrisy. I think the tale of the tape will be the next few days, whether or not Governor Sanford is sincere in his repentance," Davis told ABC television on Thursday.
About three weeks ago, Sanford lost a court battle to reject the federal stimulus money. A few days later, his wife kicked him out of their home to begin a "trial separation" with hopes of reconciling.
Then on Monday, lawmakers and reporters started questioning where the governor had been for five days. His aides said the outdoorsman was on a hiking trip in the eastern U.S. to wind down from a grueling legislative session.
But on Wednesday the governor held a rambling, tearful news conference in which he finally revealed the truth: "I've been unfaithful to my wife." His family did not attend.
The 49-year-old ruminated on God's law, moral absolutes and following one's heart. He said he spent the last five days "crying in Argentina."
Sanford described the woman who lives in Argentina as a "dear, dear friend" whom he has known for about eight years and been romantically involved with for about a year. He said he has seen her three times since the affair began, and his wife found out about it five months ago.
The Argentine woman has been identified by South American media outlets as Maria Belen Chapur, a 43-year-old divorcee with two sons. (She has also been identified by the name María Belén Shapur, a slightly different spelling.)
According to various media reports, Chapur is well educated and attractive and speaks multiple languages. Though Argentine media reported that Chapur works for an agriculture company, that appears to have been inaccurate, as The Post and Courier reports.
Sanford denied instructing his staff to cover up his affair, but acknowledged that he told them he thought he would be on a hiking trip in the U.S. and never corrected that impression after leaving for South America.
"I let them down by creating a fiction with regard to where I was going," Sanford said. "I said that was the original possibility. Again, this is my fault in ... shrouding this larger trip."
The State newspaper in Columbia published steamy e-mails between Sanford and the woman. Sanford did not identify her, nor did he answer directly whether the relationship with the Argentinian woman was over.
"What I did was wrong. Period," he said.
Now the people of South Carolina and national Republican leaders are picking up the pieces.
Mississippi Gov. Haley Barbour took over leadership of the Republican Governors Association after Stanford resigned from the post. In little more than an hour after his announcement, other Republicans were backing away from him: the Value Voters Summit dropped him from the lineup for its September roundup of Republican notables.
Political experts expect little from his last 18 months in office, and certainly not with the Legislature he's fought with for years.
"Truth be told, over the past few years, he has soured his relationship with the Legislature so much that he hasn't been particularly effective at getting an agenda through," said Scott Huffmon, political scientist at Winthrop University.
For now, Sanford's looking at the basics.
"Over the time that I have left in office, I'm going to devote my energy to building back the trust the people of this state have placed in me," Sanford said.
It will be a tall task. While some South Carolinians said they appreciated Sanford's eventual candor in admitting to his affair, the tawdry news surprised many.
"I was shocked, shocked," said Tom Daly, 42, a magazine editor in Charleston. "First of all he's a Republican golden boy and he's a strict, staunch conservative."
As Sanford awaits the political fallout, longtime friend and political aide Tom Davis said he thinks the governor can weather the storm, saying South Carolinians had a "tremendous capacity for forgiveness."
"Now, I think the South Carolina people also have a fine nose for hypocrisy," Davis said on CBS' The Early Show Thursday. "So the next few days are going to tell the tale about whether or not governor sanford is sincere in terms of taking responsibility for his actions, and the pain he's caused the people."