Investigators are using video surveillance, fingerprint technology and DNA evidence to try to identify the woman who was fatally burned by another passenger inside a subway train on Coney Island three days before Christmas, Eric Gonzalez, the Brooklyn district attorney, said on Friday.

Mr. Gonzalez also said that prosecutors had charged Sebastian Zapeta-Calil, 33, with first-degree murder for the Sunday morning attack. The police said he used a lighter to set the woman’s clothing on fire while she was sleeping on the train at about 7:30 a.m.

She died from the burns and smoke inhalation in a gruesome incident that was recorded on cellphone video, capturing the screams of bystanders and spreading rapidly across social media.

“It’s a priority for me, for my office, for the police department to identify this woman so we can notify her family of what had happened to her,” Mr. Gonzalez said during a news conference on Friday outside of Kings County Supreme Court.

Earlier on Friday, at a brief hearing, prosecutors said that a grand jury had indicted Mr. Zapeta-Calil on Thursday on one count of first-degree murder, three counts of second-degree murder and one count of arson.

Mr. Zapeta-Calil did not appear at the hearing. His lawyer, Andrew G. Friedman, did not immediately respond to a request for comment.