Doug Weigel also said on Thursday it was good that some GM executives had been fired as a result of some 2.6 million cars being recalled for the faulty ignitions that caused some cars to suddenly stall on the road, with the loss of power steering and brakes.
Barra said an internal report had found incompetence and neglect, but not a cover-up after GM took more than a decade to recall cars with faulty ignitions that caused some cars to suddenly stall on the road.
"Those people took decisions that killed people," Weigel said. His daughter Natasha, 18, and her friend, Amy Rademaker, 15, were riding in a 2005 Chevy Cobalt —- a now-recalled model — when the car suddenly lost power and slammed into trees on a rural Wisconsin road on Oct. 24, 2006.
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"GM needs to take responsibility," Weigel said.
GM has never released the names of the 13 victims, but Rademaker, who was in the front passenger seat, is known to be on the list. Weigel, who was in a back seat, is not.
Asked about a compensation fund set up by GM and administered by Kenneth Feinberg, a Washington lawyer who has run several other high-profile funds, Weigel said: "My lawyer has talked with Ken Feinberg and he told him it is not fair compensation."
In a separate telephone conversation, Weigel attorney Bob Hilliard acknowledged he had talked with Feinberg and that the offer was "not fair. I will wait to see how the plan works and then evaluate it."
He did not say how much the offer was but added, "I am conservatively hopeful, perhaps skeptical, that it will be appropriate."
Feinberg later told NBCNews.com that he spoke with Hilliard earlier on Thursday, but gave no indication of the size of compensation he was considering. He said he intended to "reach out" to Hilliard and other lawyers and interest groups as well as GM, to figure out how the process will work.
Feinberg said he hoped to begin accepting claims on Aug. 1.
The family of Brooke Melton, a 29-year-old Georgia woman who died in a crash allegedly caused by a defective ignition switch, had settled with GM in 2013, but asked a court to reopen their lawsuit last month because they said new evidence showed GM hid documents and a company engineer lied under oath. The Meltons’ attorney, Lance Cooper, has not revealed the amount of the initial settlement, and is asking for more money from the carmaker. A spokesperson for Cooper’s firm said Thursday that GM has not made a new financial offer.
Hilliard said that besides Weigel, he also represented the families of 70 people killed in crashes of GM cars that have been recalled, another 90 people catastrophically injured and some 500 people less severely injured. GM has so far only acknowledges 13 deaths in the faulty ignition case.
Commenting on Barra's press conference, Hilliard said he took her at her word and congratulated her "on her firm and strong stance on behalf of my clients and others injured and killed.
"However, I call on Ms. Barra to immediately instruct her legal staff to withdraw all GM legal filings where it has placed the obstacle of bankruptcy between my clients and justice."
GM has filed documents demanding cases be dismissed as a result of bankruptcy, he said, referring to the automaker's emergence as a new company after filing Chapter 11 bankruptcy several years ago,