0704 GMT July 17, 2018
Its report found that 28 people had died and 45 others had suffered injuries since 2006.
More than half of the 17 million vehicles sold annually in the US now have keyless ignitions.
The Society of Automotive Engineers (SAE) said it had published safety recommendations in 2011.
Director of SAE Jack Pokrzywa said, "Our standards are voluntary. It is up to the manufacturers to use them where required.”
It is difficult to put numbers on the exact number of deaths related to carbon monoxide from keyless ignitions left running as no central agency records them.
The New York Times arrived at its number from news reports, lawsuits, and police and fire records tracked by advocacy groups.
Keyless ignition systems — widely used in cars around the world —consist of a device that is carried by the driver, allowing them to start the car with the press of a button linked to the fob.
The car will not start if the key fob is not detected but once the car has been started it continues to run even if the device is removed from the vehicle.
In some hybrid car models, the engine may not be running when the driver gets out of the car but could come on later when batteries run low.
The recorded deaths had been caused by drivers leaving their vehicles running in enclosed garages which allowed carbon monoxide gas to get into their homes, according to the New York Times.
Some carmakers have voluntarily included warnings for drivers:
A spokesman for Toyota told the BBC, "Customer safety is always our priority and Toyota's Smart Key System has and continues to meet or exceed all relevant safety standards."
In 2015 a group lawsuit was filed in the US against 10 of the world's biggest carmakers on the issue, which described the technology as ‘deadly’. The case was dismissed by a judge, the following year.