Sanford, who was serving his final term in Congress at the time, said the two began corresponding by e-mail after meeting on the dance floor.
"There was some kind of connection from the very beginning," he told The Associated Press, adding that he advised her that night on her failing marriage.
He then met her for a coffee date in New York in 2004 during the Republican National Convention. Sanford told the AP that neither of the first two meetings was romantic.
In a tearful news conference June 24, 2009, Sanford said his eight-year-long friendship with Chapur became romantic only in the past year. In Tuesday's AP interview, he revealed the relationship turned physical during a 2008 state economic development trip to South America, a trip for which he is reimbursing state money used on his tickets and other expenses.
"Now,I am frightened," he told the AP, describing his state of mind after the first physical encounter. "It was before safe. But now it's not safe. We gotta put the genie back in the bottle."
In impassioned e-mails -- obtained by The State, South Carolina's largest daily newspaper -- Sanford agonized over the two's "hopelessly impossible situation of love," as Chapur wrote, "You are my love. ... Sometimes you don't choose things, they just happen. ... I can't redirect my feelings, and I am very happy with mine toward you."
He continued to insist he did not use money from state coffers to finance his romantic trysts. He told the AP he flew coach for his two meetings with Chapur in New York last year, and paid for hotels in cash. Last week, he said he would reimburse the state for last year's commerce trip, but insisted he didn't do anything illegal.
On Monday, Sanford made his second appearance after the announcement at a state budget board meeting. He apologized again to his staff for "letting you down" and said he was sorry about the affair. He also reaffirmed his decision to stay in office.
Chapur publicly acknowledged their relationship Sunday in a statement read on Argentine TV.
Chapur remains under the radar because of intense media scrutiny surrounding her. But in a brief statement conveyed through a television report on Buenos Aires' C5N channel, she said she indeed was involved with Sanford and that the published e-mail correspondence between the two was obtained from her account by a "hacker."
The former journalist did not directly acknowledge the affair or mention the embattled governor's name, saying she won't speak about her private life, which has already been made too public and painful. But her statement offered extensive details about how "the author of this evil action" broke into her e-mail account. She denied that the hacker was a friend of hers.
Chapur's friends and colleagues told ABC News she is a sophisticated and intelligent woman, and that the relationship between the two was simply a matter of love.
ABC News' Lisa Fletcher, John Hendren and The Associated Press contributed to this report.