The union says trains struck and killed one person a week last year.
The union is urging its members to slow down to about 10 miles an hour, even if it adds time to their trip.
In response, the MTA issued a statement saying, "There are other, more effective ways of making the system safer than slowing down train service. We are committed to working towards them."
The agency said there was no indication that two recent high-profile track deaths, in which passengers were pushed onto the tracks, were caused by excess speed.
Get Eyewitness News Delivered