The family of one of 33 miners trapped underground in Chile is suing the mine owners and government inspectors.
Amid the lawsuit announcement, a judge ordered $1.8m (£1.2m) of the mine's assets frozen to cover possible compensation costs.
The family accuse the owners the San Jose mine of safety lapses and officials of negligently allowing it to reopen in 2008 following an accident.
A newly-released video shows the first pictures of conditions underground.
In it, the miners appear to be in good spirits as they show how they have organised life in their refuge.
Health Minister Jaime Manalich said the miners, trapped some 700m (2,300ft) beneath the surface near the northern city of Copiapo since 5 August, had reacted calmly to the news that it could take four months for them to be rescued, according to the AFP news agency.
Remberto Valdes, a lawyer representing the family of miner Raul Bustos, told the BBC that the criminal action by Mr Bustos's family sought specifically to see the mine owners and government inspectors condemned for their alleged responsibility.
"I'm not thinking of monetary compensation," said Carolina Narvaez, the wife of Mr Bustos, according to AFP.
"I'm thinking of holding people responsible. Not only the mine's owners but also people who didn't do their job" checking the safety of the mine, she added.
Inspectors from Chile's National Geology and Mine Service - known as Sernageomin - have been named in the case because they authorised the mine to reopen in 2008, a year after it was shut following an accident.
The owners of the San Esteban Mining company which operates the San Jose mine, Alejandro Bohn and Marcelo Kemeny, have denied any responsibility for the accident.
"Now is not the the time to take the blame nor to ask for pardon," Mr Bohn said.
The judge who ordered San Esteban Mining's assets frozen said he was doing so as a precautionary measure, in case the firm has to pay compensation.
Chile's Congress is investigating the accident and President Sebastian Pinera has vowed to punish anyone found to be responsible for what happened.
Officials had delayed breaking the news of the long-term rescue out of concern for the miners' mental well-being.
Authorities have been explaining how they intend to keep the men in good physical and mental health while a shaft is drilled to rescue them from their refuge in the mine.
Their families have been holding vigils and sending the men mementos and messages down a small supply shaft.
Their growing despair turned to jubilation on Sunday when rescuers made contact with the miners via a probe lowered into the mine.
A special exercise and recreation programme is being set up to keep the men fit during their long wait.
They will also need to be in shape to be pulled up the 66cm (26-inch) wide shaft that is being bored to rescue them. Officials have warned it may take up to four months to complete.
"We were able to tell them... they would not be rescued before the Fiestas Patrias [Chile's Independence Day on 18 September], and that we hoped to get them out before Christmas," Mr Manalich was quoted as saying.
Although they took the news calmly, he said, "a period of depression, anguish and severe malaise" was possible.
The health minister added that the surface team wanted the trapped miners to set up routines, entertain themselves and attempt to simulate day and night.
The US space agency, Nasa, has been called upon for its expertise keeping astronauts alive and well on long missions in confined spaces.
The miners, who spent 17 days surviving on emergency supplies designed for a couple of days, are now being sent down the supply shaft high-protein, high-calorie foods similar to those designed for astronauts.
Other supplies have included small lights, eye patches and medicine. Anti-depressants would be included with the supplies, the health minister said.
An intercom cable has been dropped to them to allow communications with their rescuers and families.