Mark Dickey, 40, was on an international exploration mission in the Morca cave in the Taurus mountains when he began suffering gastrointestinal bleeding, Turkey's TUMAF caving federation said in a statement.
"Several international teams, including Croats and Italians, are aiding in the operations. The guy is some 1,000 meters deep, they are dividing the ascent in seven sections," TUMAF head Bulent Genc told Reuters.
"They expect (rescue operations) to take 10 days, but it may be shorter if the guy's better or longer if his situation worsens," Genc said, adding that Dickey's condition had improved and he was now able to stand on his own.
TUMAF said a phone line to reach a depth of 1,040 meters had been set up and that Croatian rescuers were setting up an additional "CaveLink" communications system as backup.
It said medics at the scene would decide whether it was possible for Dickey to be pulled out without a stretcher.
Footage from the rescue operation showed Turkish and international teams setting up tents and cables outside the sinkhole, Turkey's third-largest, which is at an altitude of 2,140 meters (7,020 ft).