But Barra said an internal investigation into why the company did not act on the problem for 11 years concluded there had been no concerted effort to hide it, but showed instead a "deeply troubling" history of failure.
She said the company would take full responsibility for the problem, only revealed in a huge recall earlier this year, and was setting up a compensation fund for victims of accidents tied to the faulty ignitions.
"The Cobalt saga was riddled with failure," she told a meeting of company employees, referring to the main car model affected by the problem.
"We misdiagnosed the problem from the very beginning... We have to own this problem."
Barra said she "was deeply saddened and disturbed" by the report by former US attorney Anton Valukas, recruited by the top US automaker to find out why it took so long for the ignition problem to come to light.
The report showed many people in the company had been aware of the problem, in which ignitions could be easily jolted into the off position while a car was still running, shutting down power steering and the safety airbags.
The company has said it knows of more than 30 accidents where the ignition problem led to non-deployment of the airbags, and 13 deaths.
The US auto safety regulator, the National Highway Traffic Safety Administration, said it thinks the death toll could be higher.
And the independent Center for Auto Safety said it had counted more than 300 deaths linked to airbag non-deployment in the GM cars covered by the ignition recall, though it has not linked that problem to ignition shutdowns.
GM is facing a federal criminal probe and a congressional investigation for not having recalled the cars years ago, and victim lawsuits that could total in the billions of dollars, according to analysts.
Barra would not say how the compensation, currently being studied, would be awarded.
However, she said, "We are going to do the right thing for the affected parties."
She said the Valukas report showed a history of management deficiences and poor judgments, with numerous company employees touching the issue but none seeing a significant problem or taking it to top management.
"Pieces of information and clues did not get put together," she said.
"No one took responsibility."
Even so, she said, the Valukas report found there was "no conspiracy by the corporation to cover up facts."
It also cleared her and GM executive vice president Mark Reuss, her right-hand-man, of blame in the saga.
Barra became chief executive on January 15 after a lifetime career in various positions in the company.
One month later the company began the recall of some 2.6 million Cobalts and other models from the 2004-2011 model years for ignition problems.
Since then GM has plumbed deeply into its safety files and initiated recalls of more than 15 million cars, in an effort to ward off fresh scandals and begin rebuilding the company's battered reputation.
Barra said there are likely more recalls in store in the near future, and that an "aggressive" stance on product recalls is "the new norm" at GM.
She told employees that it was now unacceptable to not speak up about a safety problem in GM cars.
"We need to hold each other accountable," she said.
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