General Motors Co. Chief Executive Officer Mary Barra said on Tuesday that the nation's largest auto maker likely would provide shareholders an estimate of the financial fallout from a recall tied to a troubled ignition switch by early next month, reported The Wall Street Journal.

Ms. Barra said the company would have a better sense of the costs facing it after Kenneth Feinberg, a compensation expert hired to advise the company, provides measures of how accident victims or their families will be compensated. Mr. Feinberg could provide that update within the next few weeks.

"At that point we will make an estimate," Ms. Barra said ahead of the company's annual shareholders meeting at its Detroit headquarters.

It is unclear if GM will immediately share that figure or wait until its second-quarter results are released July 24. The company will begin accepting claims from victims on Aug. 1.

Estimates for the price GM could pay to compensate victims, legal fees and any settlements or judgments range from less than $5 billion to as much as $7 billion.

GM has said it would create a compensation fund for victims of crashes related to a defective ignition switch, which could slip out of the run position, causing the car's air bags not to deploy in crashes. Analysts say GM could face additional fines over its delay in acting on the defect and notifying safety regulators. The company's actions are under investigation by the Justice Department and the Securities and Exchange Commission.

Ms. Barra declined to say if the company would increase the charges it has taken to this point to cover the costs associated with a variety of recalls. GM has already taken a charge of $1.7 billion for recalling and repairing 2.6 million vehicles equipped with potentially defective ignition switches along with other vehicles for other potential safety problems.

Shareholders gathered in Detroit on Tuesday for an overall business update and any details on how the ignition switch recall, fines and investigations would affect the auto maker's balance sheet.

The company released an internal report last Thursday that cleared Ms. Barra and her executive team of any wrongdoing but criticized the company for a corporate culture built on shirking responsibility and management inaction. The company dismissed 15 people and disciplined five others.

"We feel we have taken the appropriate action as it relates to the ignition switch recall," Ms. Barra said when asked if more action will be taken against employees.

Separately, Ms. Barra said the company continues probing all of its car-safety reviews but she deemed as unlikely finding another problem akin to the ignition switch. GM engineers discovered the defective switch in 2004 but didn't initiate a recall until February of this year.

"I have nothing to conclude there is anything like this, and we have been digging pretty deep and as issues are raised we will continue to do that," Ms. Barra said.

She said GM employees are "owning" the mistakes made in the ignition-switch recall and that she has received hundreds of emails from employees offering support and some flagging other problems within the company. Ms. Barra declined to identify those issues.

Meanwhile, the executive director of safety advocate Center for Auto Safety criticized the National Highway Traffic Safety Administration for failing to move against GM although the auto maker was racking up 20,000 to 30,000 stalling incidents in Chevrolet Cobalts and other vehicles.

"Never has a regulatory agency had so much information on such a lethal defect and done so little to protect the public," Clarence Ditlow said. "People died because GM concealed the defect and NHTSA failed to act."

Mr. Ditlow's comments come as Ms. Barra prepares to return to Capitol Hill as early as next week. Ms. Barra had promised to update lawmakers once the internal report was completed. Congressional leaders are investigating both GM and NHTSA for their failures in the ignition-switch recall.