In congressional testimony on Wednesday, Mary Barra said General Motors would not compensate drivers for economic loss related to a recall of 2.6 million small cars earlier this year.

The automaker's compensation fund will go toward those injured in crashes and families of the people who died, Edmunds.com reported. Barra specified that the fund "is for those who lost loved ones or who suffered serious physical injury," as quoted by Edmunds.

Defective ignition switches in the Chevrolet Cobalt, Saturn Ion and other models have been linked to at least 54 crashes and 13 deaths.

Owners who claim economic loss related to the recall will have their claims addressed in court, Barra said. GM has been hit with more than 70 such lawsuits.

Nearly 200,000 vehicles have been repaired of the 2.6 million included in the recall, according to Barra, who said that repairs should be completed by early October.

"The challenge is getting the customer in for the repair," she said. "We've done research to figure out which messages would be most compelling."

Barra, who earlier provided testimony in a federal hearing for an investigation into GM, was asked Wednesday to explain GM's steps for restitution following the recall, NBC News reported. Along with the compensation fund, Barra detailed GM's internal investigation and the decision to fire 15 employees connected with the problematic switches.

Right before Barra's congressional testimony on Wednesday, family members of those injured in GM vehicles spoke at a news conference, restating their demands that GM let victims reopen closed claims and compensate those injured without caps or time limits.

"GM needs to accept responsibility for what it's done and do what's right," said Robbie Buzard, whose son Trenton was paralyzed in an accident in 2009, as quoted by NBC News. Trenton was a passenger in a Chevrolet Cobalt when he was hit by a drunk driver near Pittsburgh; his great-grandmother, who was driving the Chevy, was killed.  

GM has tapped attorney Kenneth Feinberg, known for assigning compensation after high-profile events such as the 9/11 attacks and the Boston Marathon bombings, to oversee the compensation fund. 

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