(CNN) -- Virtually all of the miners who were trapped for 69 days in a Chilean mine last year have filed a lawsuit against the government, seeking more than half a million dollars each in damages.

A lawyer representing 31 of the 33 miners says he filed the civil suit Friday at a Santiago court.

The lawsuit, the miners say, is not about the money, but about setting a precedent so that such an accident does not happen again. On August 5 of last year, a cave-in at the San Jose mine trapped the 33 for months in an ordeal that ended with their heroic rescue.

The lawsuit accuses the government agency that oversees mining of failing to ensure safety measures, CNN Chile reported.

"This lawsuit is only to set a precedent so this won't happen again," said miner Omar Reygadas. "It's so that conditions improve."

The miners are demanding $541,000 each, though some miners said they did not know the amount of money until they read about it in the media.

Reygadas, in an interview with CNN Chile, said that he was not even aware that their attorney was filing a lawsuit against the government. He thought it was a lawsuit against the owner of the mine.

The lawsuit is not a slap at the government of President Sebastian Pinera, whose team coordinated the rescue, Reygadas said. Rather it was at the state in general for allowing the conditions that led to the accident, he said.

But while the miners said that money wasn't the primary goal, Reygadas said that it would be helpful to a majority of them.

"There's a myth that us miners have a lot of money, but that is not the truth," he said.

In the aftermath of the rescue, the miners received donations and assistance that totaled to more than $17,000 each, he said. Some have been able to pad that with income from motivational speeches.

But they have not been able to work since the mine incident because of psychological issues, Reygadas said.

It is true that the miners have been treated to all-expense paid trips around the world as they basked in the fame of having survived their ordeal, but they didn't make money off it, he said.

"For us to have become millionaires, we would have had to find a jackpot of gold inside the mine and brought it up with us," he said.

Reygadas estimated that a "majority" of the miners had money problems, "some more than others."

On the same day that the lawsuit was filed, Reygadas and four other miners went to the presidential palace to invite Pinera to attend a Mass and observance of the year that has passed since the accident.

The miners are still very grateful to Pinera for his leadership during the rescue, he said.

Pinera has said that the operation to rescue the miners cost between $10 million and $20 million.

A spokesman for the Chilean government was not available Saturday to comment on the lawsuit.

At the time of the collapse of the mine, Mining Minister Laurence Goldborne said mining laws were not to blame for the disaster.

"The problem was that the owners did not do what they were told to," he told CNN in September. "Not because it was too expensive or they were greedy, but just because they didn't care. ... We have got good regulations but maybe we need to improve auditing of those regulations."

Later, Pinera said Chile would adopt stricter safety standards that are more in line with those practiced in the United States. And, he said, the government would ensure that tougher regulations are enforced.