The incident - which occurred mid-morning on the A train line between two stations in Harlem in northern Manhattan - left 36 people with minor injuries, the spokesman told AFP. Thirty-four people suffered minor injuries.
Authorities say a train near the 125th Street station automatically activated its emergency brakes, causing two of eight cars to derail.
The cause of the derailment, which continued to disrupt traffic throughout the day, was not immediately clear. Asked about the safety of the system, Mr. Lhota said he wanted to "rebuild the confidence" in the agency.
"Mostly everyone was shaken up and nerves frayed, but once we started walking there was smoke, so people started coughing", said Craig Sheil.
The Fire Department New York (FDNY) said the smoke was caused by rubbish setting on fire.
Transit officials say a preliminary investigation shows that the derailment was caused by an improperly secured piece of replacement rail that was on the tracks.
During an interview last month on CNBC, the Democratic governor said the federal government was to blame for not responding to the state's requests for transportation funding, leaving NY "way behind" on infrastructure.
The South Ferry station on the No. 1 line reopened after $340 million worth of repairs.
Dozens of people were hurt Tuesday morning in NY when a subway derailed in Manhattan. Officials said most of the injuries involved smoke inhalation and none were life-threatening. He said there was white smoke and "there was a lot of banging around in that vehicle - it was really bad". Emergency crews shut off track power after derailments to prevent evacuees from being electrocuted.
Julian Robinson said he was stuck on one of them for about an hour before rescuers arrived to escort passengers along the tracks into the station.
Transit workers in hard hats cheered as the yellow tape blocking the entrance was removed.
Riders had to use an older, outmoded station that only had room for the first five cars of a 10-car train during the lengthy fix process. The subway station was subsequently evacuated.
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.