They want Cuomo to "fund and fix" the system that carries almost 6 million riders a day, the organizers, Riders Alliance, a public transportation advocacy group, said in a statement.
The MTA added that three disabled trains had been evacuated and passengers were taken safely above ground.
Passengers on the A train said it suddenly jerked and began shaking violently as it approached the station at 125th Street and St. Nicholas Avenue.
At least 34 people had injuries including smoke inhalation, though all were expected to be OK, fire officials said.
Riders told of smoke and fire on the tracks, which Lhota explained could have resulted from litter igniting after the crash.
According to the Metropolitan Transportation Authority, service was suspended or rerouted on several subway lines running between upper Manhattan and northern Brooklyn following the accident.
Joe Lhota (LOH'-tuh) says there were no initial indications of equipment or track failure before two cars derailed and scraped a wall on Tuesday morning.
Not to mention other derailments and issues that are frustrating riders.
MTA Chairman Joe Lhota said the derailment happened after emergency brakes were applied.
The No. 1 train prepares to leave the South Ferry Station, Tuesday June 27, 2017, in NY.
A New York City subway train derailment that injured dozens of people on Tuesday was caused by "an improperly secured piece of replacement rail", Metropolitan Transportation Authority officials said. The station reopened Tuesday, almost five years after it was flooded by Superstorm Sandy in October 2012.
Photos and videos posted on social media by terrified straphangers give an insight into what happened.
"People were panicking, jumping out of their seats, just crying and praying out loud", said another passenger. He said he didn't know yet if a passenger had pulled the emergency brake.
The number of delays has soared this year and many commuters complain that they no longer can be sure they will be able to get around the city reliably. A report released earlier this month found that rush-hour cancellations and delays on the railroad are at the highest level in ten years.