(Bloomberg) - General Motors Co. (GM) CEO Mary Barra, under fire for the company’s slow response to flawed ignition switches linked to 13 deaths, said she is creating a team that will make the company’s cars as safe as they are fun to drive.

“This new organization will build on the formula and specific actions we have taken in recent years” to make GM’s cars the best to drive in the industry, Barra said during an event in advance of the 2014 New York International Auto Show. “We will mirror this approach to focus on safety performance.”

The new global product integrity organization will report to Mark Reuss, head of product development, and include the new team headed by Jeff Boyer, the vice president for vehicle safety, she said. Barra spoke at a forum hosted by J.D. Power & Associates and the National Automobile Dealers Association (NADA). She and other GM executives are in New York as the automaker introduces new vehicles before the show.

The speech was Barra’s first public appearance since being grilled at U.S. congressional hearings on April 1 and 2. A House panel released more than 700 pages of documents that shed new light on why it took the Detroit-based company so long to recall 2.59 million small cars with potentially faulty ignition switches linked to at least 13 deaths.

Growing Crisis

Barra is struggling to contain the growing crisis that’s consumed much of her first three months on the job since she succeeded Dan Akerson as CEO on Jan. 15. She has said GM failed to act quickly enough and apologized for the deaths.

As it plays defense on the recall drama, which began Feb. 13, GM is also trying to garner publicity for new vehicles it’s bringing to the market this year. The automaker is showing changes to its 2015 Chevrolet Cruze compact car for the U.S. market, including a new front end that takes styling cues from the larger Impala and revised cup holders. GM also is showing the convertible version of the Corvette Z06 sports car.

GM also announced it will bring the Chevrolet Trax sport-utility vehicle to the U.S. Essentially a Chevy version of the Buick Encore compact SUV, the 2015 Chevrolet Trax will be the brand’s seventh small-vehicle introduction in less than four years in the U.S., the company said. The Encore, which is also sold as an Opel Mokka in Europe, went on sale in the U.S. last year.

Progress ‘Overshadowed’

Barra focused the first part of her speech on the progress the company has made including raising transaction prices, increasing retail market share in the U.S. and boosting sales in China.

“I think it’s fair to say that much of the progress we have made in the last two months has been overshadowed by the intensity of the recall coverage - but in fact there has been a lot of good news to report,” Barra said.

GM rose 1.8 percent to $33.97 at the close in New York. The shares have declined 4.5 percent this year since Feb. 12, the day before the ignition-switch recalls were announced.

Barra is also beginning to shape her executive team, with GM announcing April 14 that John Quattrone, a key deputy of hers who ran human resources for product development when she was head of the department, was named the new senior vice president of global human resources. GM also announced that Selim Bingol, head of GM’s public relations and global public policy operations, was leaving. A replacement wasn’t announced.

Bob Ferguson, who ran government relations and public policy before taking over Cadillac in 2012, is now running both the luxury brand and public policy, Barra told reporters later at a Chevrolet press conference.

Speak Up

Barra announced last week a program to recognize employees for speaking up about safety concerns and has suspended with pay two engineers involved in the development of the recalled cars.

“We agonized over that decision, but we felt it was right for the individuals and right for the company at this time,” she said of putting them on leave. Barra stepped around a question about what it might mean if more GM employees were discovered to be involved. “I don’t want to speculate on any aspect,” she said. “Let’s be really, really clear, these are real people with real careers.”

Barra reiterated that she is “focused on truth and then taking the right actions.”

After her presentation at the Auto Forum, Barra was swarmed by dozens of reporters and camera people as she walked off stage and tried to leave the ballroom. Reuss and aides worked to block Barra from the crush as spokesmen yelled for the crowd to back away.

Valukas Report

GM in March announced it hired Jenner & Block LLC Chairman Anton Valukas, who served as a Justice Department-appointed examiner of the downfall of Lehman Brothers Holdings Inc., to help lead the automaker’s internal probe along with GM General Counsel Michael Millikin.

The internal investigation remains on track to take 45 to 60 days, she told reporters yesterday after the presentation. She said she is not aware of any documents having been given to the U.S. Justice Department.

Barra has also asked for a review by lawyer Kenneth Feinberg, who determined compensation for survivors of the Sept. 11 and Boston Marathon terrorist attacks, on what GM should do for victims of the crashes. The automaker is currently shielded from paying claims for accidents prior to July 2009 as part of its bankruptcy terms.

Regulator Relations

The U.S. National Highway Traffic Safety Administration (NHTSA) said last week it’s fining GM $7,000 a day for failing to respond to one-third of requests for information about the recall with an April 3 deadline. An agency lawyer called an internal company probe the automaker cited as reason for the delay “irrelevant” and threatened to refer GM to the Justice Department.

GM has a team dedicated to working on the NHTSA questions, Barra said. “We work on those every day,” she told reporters. “We are trying to be as responsive as possible. But we will not sacrifice the accuracy.”

The automaker has produced 21,000 documents totaling more than 271,000 pages that span a decade to NHTSA, according to GM.

In documents released last week, GM officials expressed shock that the regulator described the company as “slow to communicate, slow to act” and harder to deal with than other automakers.

Boyer is having regular discussions with NHTSA officials about ways for the company to do better, Barra said. “They made some suggestions to us on how we can improve and we’re implementing them immediately.”

SNL Target

Her performance before Congress two weeks ago became the butt of jokes on NBC’s “Saturday Night Live,” which mocked her elusiveness in answering questions. The NBC show opened with a parody of the hearings, with cast member Kate McKinnon as Barra answering questions using dodges like “we’re looking into that” and “that’s part of our investigation.” “That was the old GM. I can only speak to how the new GM would handle it,” McKinnon said gravely, adding, “OK, it’s the new GM starting ... now.” Later she said, “Your honor, may I approach the exit?”

Asked about the sketch, Barra said she’s watched the show most of her adult life.

“It’s important to maintain your sense of humor,” she said. “But I can tell we are very serious and very dedicated to doing the right thing for our customer.” Asked how McKinnon did playing her, Barra demurred. “Again, there are probably better people than me to judge.”