"I don't know how she happened to resist that long," said rescue worker JP Malaganne.
The 16-year-old was found in the rubble of a house near the College St Gerard, which one of her relatives said she had just started attending.
Neighbours had been searching in the rubble of their homes in the central Carrefour-Feuilles district when they heard a weak voice and called rescue teams to help.
They managed to locate the girl in the wreckage and less than an hour later had dug a hole to pull her out, covered in dust.
Rescuer Claude Fuilla told the Associated Press news agency: "She couldn't really talk to us or say how long she'd been there but I think she'd been there since the earthquake.
"I don't think she could have survived even a few more hours."
Darlene was given water and oxygen before being taken to a French field hospital and medical ship.
"She just said 'Thank you', she's very weak, which suggests that she's been there for 15 days," said Samuel Bernes, head of the rescue team that discovered her.
He described her location within the rubble as "in a pocket, surrounded by concrete".
The BBC's Karen Allen, in the Haitian capital, said that rescue workers had told her the teenager was trapped in the bathroom when the quake struck and was able to survive by drinking water from a bath.
On Tuesday, rescuers discovered a 31-year-old man who had been trapped for 12 days after being caught in one of the numerous aftershocks that rocked the city after the earthquake.
In announcing the election delay, Mr Preval said he would not seek to remain in office beyond the end of his term in February 2011.
He added: "I don't think the time is right to hold elections now given the conditions in which people are living."
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