Dilip Joseph's employers, Colorado-based Morning Star Development, insisted that it did not pay any ransom to the Taliban for the release of the doctor, who worked with it for the last three years and has been a frequent traveller to Afghanistan.
He would soon return to his home in Colorado, they said.
"Dilip Joseph is still in Afghanistan and will be coming back soon," the Morning Star Development executive director, Lars Peterson, said.
"He oversees our medical clinics in Afghanistan, teaching and preparing the local doctors and midwives in their work. I have not spoken to him since last week so I don't know much more about his condition," Peterson said.
The family of Joseph was not available for comment.
"His family is asking for privacy at this time," he said.
Peterson said Joseph along with two other members of the Morning Star Development were kidnapped by the Taliban on December 5.
He was rescued in a joint operation by US commandos and Afghan forces. While one US Navy SEAL was killed in the rescue, seven insurgents were also left dead.
"Morning Star Development is grateful beyond words for the assistance and support of many people and organisations during this event. Due to security concerns, some cannot be named but their help will never be forgotten.
"Among these who cannot be named we include all of the courageous members of the US military who successfully rescued Mr Joseph as they risked their own lives doing so," he said in a statement.
The other two members were released by their captors about 11 hours earlier following hours of negotiations conducted over three days.
The three staff members were abducted while returning from a visit to one of our rural medical clinics in eastern Kabul Province.
"They were stopped and captured while driving, by a group of armed men. They were eventually taken to a mountainous area about 50 miles from the Pakistan border," he said.
Contact between the hostages, their captors, and Morning Star's crisis management team (operating from Kabul and Colorado Springs) began almost immediately and continued in an on-again, off-again pattern until early Saturday evening (Afghanistan time), he said.
"It was at about that time that the captors released two of the three hostages. These two hostages are national staff members of Morning Star Development.
"One is a member of the organisation's medical staff and the other is a member of the organisation's support staff," he said without diclosing their identity as they live and work in the general region of the event.
Peterson said Joseph remained in the custody of his kidnappers after his colleagues were released and later that night, US military forces rescued him. He was then taken to Bagram Airfield north of Kabul.
Though he was reported to be in good condition and uninjured during the rescue, he will receive precautionary examinations and debriefing before returning to his Colorado Springs home, probably within a few days.
His family was notified of his safe rescue very shortly after he was freed.
"Morning Star Development does state categorically that we paid no ransom, money or other consideration to the captors or anyone else to secure the release of these hostages," he said.
Washington: After being rescued in a daring military operation from Taliban captivity, an Indian American doctor who was involved in training local medical professionals in Afghanistan, is set to return home.
First Published: Tuesday, December 11, 2012, 16:26