Excerpts of the 45-minute video released Thursday showed the men upbeat despite their 21-day ordeal in a hot and dank underground shelter, where they await a potentially months-long rescue.
"We've organized everything really well down here," said one of the miners, sporting a scraggly beard and pointing to a corner reserved for medical supplies.
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"This is where we entertain ourselves, where we have a meeting every day, where we make plans. This is where we pray," he added in a video aired on Chilean television after it was shown to families of the 33 miners.
About a dozen other miners waved at the mini-camera, which was lowered earlier 700 meters (2,300 feet) below the surface via one of the metal capsules that have been ferrying supplies to them since Sunday.
On Monday, the first brief, shadowy images of a miner's face were sent from a rudimentary camera initially lowered to the shelter.
The discovery of the miners still alive three weeks after a cave-in triggered mass celebrations in Chile, where mining is a vital industry.
The country is the world's top copper producer, with one third of total output, and in their video, the miners appeared eager to claim a position of respect for the thousands of Chileans who toil underground.
"Here, ladies and gentlemen, there are professionals. We have electricians, we have mechanics, there is our leader who is a very good artist, we have special machine operators," one of the miners said in the video.
"These are no longer the miners of 100 or 150 years ago.... These are miners you can be proud of."
San Esteban Mining, the owner of the gold and copper mine in northern Chile, was ordered Thursday by a local judge to freeze 1.8 million dollars in revenue so that it can pay future compensation to 26 of the families of those trapped.
Litigation against the mining company swirled as officials grew concerned about the mental wellbeing of the miners awaiting a months-long rescue.
Experts say the process of digging a rescue shaft will take up to four months to complete.
Some of the men were already exhibiting psychological "problems," Health Minister Jaime Manalich told CNN.
They were having trouble sleeping and were becoming increasingly anxious and irritable after being cramped in the confined space for so long, he said.
The men have been told to brace for an extended rescue operation, certainly more than two months, but were not given engineers' estimates that it could be twice that long.
Officials were carefully watching for any negative reaction to the news.
Rescuers also said nine of the men were "too fat" to fit through the 66-centimeter (26-inch) diameter escape shaft that would eventually reach them, according to CNN.
Medical teams on the surface said the miners lost between eight and 10 kilograms (18 to 22 pounds) before contact was made Sunday.
Still, doctors were looking at diet and exercise regimes to ensure all would be able to fit through the shaft -- roughly the diameter of a bicycle wheel -- when the time comes.
The men survived more than two weeks on meager rations and water dripping into the tunnel before their discovery last Sunday by a drill probe.
Capsules now ferry food and water to them along the probe's small hole, which also served as a conduit for an intercom cable to communicate with officials, doctors and family members.
After regaining strength, they are to begin daily exercise and engage in singing and card games to stay mentally acute.
Four officials from US space agency NASA were due to arrive Sunday or Monday in Chile to provide expertise on extended isolation in hopes of easing the miners' months-long ordeal underground.
Chilean President Sebastian Pinera has taken a leading role in overseeing the rescue.
Late Tuesday, he heard the men say they were entombed in "hell" and beg him not to abandon them.
"You won't be left alone, nor have you been alone a single moment," Pinera vowed.
He later said he was determined the men "will be with us for Christmas and New Year."
Officials who spoke to La Tercera newspaper said the rescue could cost up to 10 million dollars, with half going toward operating the hydraulic bore that will excavate the rescue shaft to the men.
The family that lodged the first lawsuit over the accident has accused the mine owners and government inspectors of criminal negligence by allowing the facility to reopen in 2008 after a worker accident led to its closure in 2007.
