Federal safety regulators received more than 260 complaints over the past 11 years about General Motors vehicles that suddenly turned off while being driven, but they declined to investigate the problem, which GM now says is linked to 13 deaths and requires the recall of more than 1.6 million cars worldwide.

A New York Times analysis of consumer complaints submitted to the National Highway Traffic Safety Administration found that since February 2003 it received an average of two complaints a month about potentially dangerous shutdowns, but it repeatedly responded that there was not enough evidence of a problem to warrant a safety investigation.

The complaints — the most recent of which was filed Thursday — involved six GM models that the automaker is now recalling because of defective ignition switches that can shut off engines and power systems and disable air bags. GM said the first recall notices were mailed Friday to the owners of the vehicles.

Many of the complaints detailed frightening scenes in which moving cars suddenly stalled at high speeds, on highways, in the middle of city traffic, and while crossing railroad tracks. A number of the complaints warned of catastrophic consequences if something was not done.

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To the mounting complaints, the safety agency sometimes responded with polite but formulaic letters similar to one it sent in December 2010 to Barney Frank, then a congressman from Massachusetts, who had written on behalf of a distraught constituent whose 2006 Cobalt kept stalling. In the letter to Frank, the agency said it had reviewed its database of complaints to determine if a “safety defect trend” existed. “At this time, there is insufficient evidence to warrant opening a safety defect investigation,” the letter concluded.

Failure to recognize a pattern in individual complaints has been a problem for the safety agency before. In the late 1990s, it was criticized for failing to detect a wave of highway rollovers in Ford Explorers with Firestone tires, a problem that was eventually linked to 271 deaths.

The safety agency has repeatedly suggested that it failed to act over the years because of a lack of a critical mass of evidence that suggested a problem beyond isolated incidents.

By the time the agency wrote to Frank in 2010, it had received more than 170 complaints.