Dr Ernest Benjamin says the woman is "critically ill"
Two people have been rescued after spending 10 days under rubble following the devastating Haiti earthquake.
Doctors say the woman, who is 84, is in a grave condition, but that they are doing all they can to save her.
And an Israeli search team pulled a 21-year-old man alive from the rubble. He is said to be in a stable condition.
The rescues came as the official government death toll from the earthquake rose to 110,000. But the search operation is almost over.
UN spokeswoman Elizabeth Byrs said some rescue teams were leaving, as they were exhausted and there was now little hope of finding more people alive under the rubble.
Those that remained were "concentrating more and more on humanitarian aid for those who need it", she said.
A benefit concert featuring more than 100 music and Hollywood stars has been broadcast around the world to raise money for the victims of the earthquake.
The 84-year-old woman survivor, rescued on Friday after 10 days in the rubble, is being treated by doctors at the main city hospital with intravenous fluids and drugs.
"I'm trying to find out how I can help her survive," Dr Ernest Benjamin said. "It's worth everything to try to save her."
Her son told the agency he had heard her cries on Thursday morning and, almost a day later, he dug her out with the help of friends.
The Israeli team which rescued the young man, Emmannuel Buso, told the Associated Press news agency that they had called out to him near the debris of his home and to their surprise, he responded.
"I felt the house dancing around me"
In an interview with AP from his hospital bed, he describes coming out of the shower when the earthquake hit.
"I felt the house dancing around me," he said. "I didn't know if I was up or down".
He described passing out in the rubble, dreaming at times that he could hear his mother's voice.
He said he had no food, and drank his own urine to keep thirst at bay.
The head of the Israeli team, Major Amir Ben David, said the rescue had given hope more people could be found alive.
In Port-au-Prince, life is slowly returning to normal, with shops opening and buses running - although many residents are continuing to leave the devastated capital.
AT THE SCENE
Christian Fraser, BBC News, Jacmel
Jacmel, a former colonial coffee town, is desperate for help. Perhaps one in three buildings in the old town now lies in ruins - more than 100 years of history, shattered in a few catastrophic seconds.
At the Saint Michele hospital the patients are lying in the garden, baking in the heat, without enough doctors to help. The hospital buildings are too unstable to use.
In the operating theatre, nurses swat flies as the surgeons do what they can. Outside, the injured scream for painkillers.
On Thursday, the government announced plans to send 400,000 people to tented cities in the countryside, to try to halt the spread of disease in the makeshift settlements that have sprung up in the capital.
Construction for the temporary centres has already started, the Associated Press news agency says, but it is unclear when they will be populated.
Aid officials say about 200,000 people have already left the city, many to stay with relatives in other parts of the country.
Some 122 people have been saved by international search and rescue teams, according to the US government.
At least 75,000 bodies have so far been buried in mass graves, Haiti's government has said. Many more remain uncollected in the streets.
An estimated 1.5 million people were left homeless by the 7.0-magnitude quake, which some have estimated has killed as many as 200,000 people.
Warning on migration
Some Haitians have tried to flee abroad, but US Homeland Security Secretary Janet Napolitano warned Haitians not to use the earthquake as an excuse to try to enter the US illegally.
Haitians need to be there to help rebuild their country, this is not an opportunity for migration
She said anyone caught trying to do so would be repatriated.
"Haitians need to be there to help rebuild their country, this is not an opportunity for migration," she said.
At least 500,000 people are currently living outdoors in 447 improvised camps in Port-au-Prince, according to the International Organisation for Migration (IOM), with limited shelter and access to water.
Western countries were hoping to boost donations for the aid effort with a multi-network telethon.
Hope for Haiti Now, broadcast from New York, London, Los Angeles and Haiti, featured Madonna, Bruce Springsteen, Beyonce and other major artists.
The concert was shown on all major US TV channels, MTV in the UK and worldwide on YouTube.
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