DETROIT — The ignition-switch scandal at General Motors widened Thursday as the automaker suspended two engineers and added another repair to its recall of cars with a faulty ignition switch that has been linked to 13 deaths.

The company is facing increasing pressure from lawmakers to warn owners of recalled cars to park their vehicles until they are fixed. And as the company scrambles to make the repairs, the financial toll of its mounting recalls continues to grow.

On Thursday, GM said it would cost $1.3 billion in the first quarter to pay for all of its recalls — a significant increase over the $750 million it had previously estimated.

GM took its first steps Thursday to discipline employees involved in the company’s failure to fix the switches, which can cause engines to shut off, disabling air bags and putting occupants at risk of serious injury or death.

Mary Barra, the automaker’s chief executive, said two engineers had been placed on paid leave after she was briefed on the results of an internal investigation conducted by Anton Valukas, a former U.S. attorney. GM did not name the engineers, but a government investigator briefed on the matter said they were Raymond DeGiorgio, chief ignition engineer for small cars like the Cobalt, and Gary Altman, an engineering manager on the small-car program.

“This is an interim step as we seek the truth about what happened,” Barra said in a statement. “It was a difficult decision, but I believe it is best for GM.”

DeGiorgio has been identified in documents as the engineer who approved a change to improve the switch in 2006. But the change was never cataloged as a new part, and GM did not recall cars with the original, defective switch.

Both DeGiorgio and Altman were deposed last year in a lawsuit filed against GM by the family of a Georgia woman who died in a Cobalt crash in 2010.

In his deposition, Altman was asked by the family’s lawyer, Lance Cooper, whether GM had made “a business decision” not to make the ignition switch stronger and less prone to failure.

“That is what happened, yes,” Altman said.

GM later settled the lawsuit. But the case is now viewed by investigators and lawmakers as a turning point in efforts by outsiders to expose what went wrong with the switches inside GM.

The company declined to make DeGiorgio and Altman available for comment.