
The latest health information was released as engineers said the second of two drills boring rescue shafts down to the 33 miners had reached a depth of 100 meters.
The men have been trapped some 700 meters (2,300 feet) below ground for more than a month, since an August 5 cave-in at the San Jose mine.
Both the ailing men are receiving medication for their conditions, officials said.
One miner had dental problems causing him "persistent pain and is receiving antibiotics," the National Office of Emergency statement said.
Another was receiving medication for hypertension, but the problem was said to be pre-existing and not caused by conditions in the mine, where the men have been trapped for 32 days.
A crew of medical experts, including psychiatrists and nutritionists, has been assembled to attend to the health of the men, who range in age from 19 to 63.
After 17 days in which the miners survived on carefully rationed cans of tuna, medical crews nursed them back to health, feeding them rehydration packs until they were strong enough to eat solid food sent down from above.
Now they get a normal diet, of some 2,400 calories a day, but have been warned to keep trim so that they will be slim enough to be fit through a narrow rescue shaft that engineers are drilling to reach them.
Two drills are already working on rescue shafts to reach the men, with a third expected to begin work later this month.
The initial drill started work on August 30, and is expected to first bore a 33-centimeter (13-inch) wide pilot hole that will then be doubled using a special drill bit to 66 centimeters.
That process could take up to four months and requires drilling down the full 700 meters (2,300 feet) into the mine.
The second drill, which began its installation phase on Sunday, still has to reach down 620 meters (2,034 feet) but would take less time. Engineers said Tuesday it had already bored down 100 meters (330 feet).
A third option involves a drill that would have to reach down just 597 meters (1,958 feet), shortening the rescue time to perhaps two months. But it won't be ready to start work until September 18.
In the meantime, experts have been working to keep the miners sane and officials have offered them multiple entertainment options.
A most recent delivery to the underground refuge housing the men included 80 letters, and with the dispatch of an audio-visual system linked up via fiber-optic cables, the miners have been able to videoconference with their relatives too.
That equipment will be put to the test Tuesday when the miners are scheduled to settle in and watch a friendly soccer match between Chile's national team and Ukraine that will be streamed live to their shelter.