Betancourt, 46, who was snatched by rebels while running for president of Colombia in 2002, met relatives of kidnapped victims to explore new ways to rescue hostages.
"It is important that we can keep counting on regional leaders to help us look for a way, an opening that will allow for the liberation of those who remain behind," the dual French-Colombian citizen who was released in July told a Bogota news conference.
"If my freedom can be good for something, I hope it helps achieve the freedom of all the other hostages," she said.
The Farc has been kidnapping people for ransom and political leverage as part of its 44-year war against the state.
Alvaro Uribe, Colombia's president, is to join Betancourt in her tour through several South American countries, including Ecuador, Brazil, and Venezuela, to discuss the ongoing problem of hostage-taking on the continent.
Betancourt was chained up in jungle camps, her health often in peril, until Colombian security forces duped rebels into handing her and 14 other captives over in a daring rescue operation.
She has lived in Europe since her rescue and says she does not wish to return to politics in Colombia.