By Natasja Sheriff

NEW YORK (Reuters) - A New York jury retired for the day without reaching a verdict on Tuesday after telling the judge it was deadlocked in the murder trial of a man accused of killing 6-year-old Etan Patz.

The judge, who responded by ordering the panel back to work, allowed the jury to go home at the end of the day but return on Wednesday to keep weighing the fate of Pedro Hernandez.

Hernandez, 54, a former deli worker, told police in 2012 that he choked Patz in the basement of a nearby deli where he worked, stuffed him in a box and left his still-moving body in an alley.

He is charged with murder and kidnapping in state Supreme Court in Manhattan. Hernandez's attorneys argued he is mentally ill and that police coerced his confession.

Patz vanished in 1979 from his Soho neighborhood in Manhattan in a case that changed the way the United States responds to reports of missing children.

His picture was among the first to appear on milk cartons in a national campaign to locate missing children.

At midday on Tuesday on the 15th day of deliberations, the jury sent the note to Judge Maxwell Wiley saying it was deadlocked. The panel sent a similar note last Wednesday.

There is no limit to the number of times the judge could send the jury back to deliberate, but at some point such instructions would be considered coercive by an appeals court, said Alice Fontier, one of the defense attorneys.

The deliberations are believed to be among the longest in state criminal court history, said David Bookstaver, spokesman for New York state's Office of Court Administration, which does not keep records on the length of jury deliberations.

Patz vanished on May 25, 1979, as he walked alone for the first time to a school bus stop.

The defense blames Jose Ramos, whose girlfriend walked Patz home from school and who was long considered the prime suspect.

Ramos, convicted of sexually abusing boys, is serving a prison term in Pennsylvania.

Patz was never found and was declared dead in 2001.

If the jury remains unable to reach a verdict and a mistrial is declared, the prosecution would have to decide whether to retry the case.

(Reporting by Natasja Sheriff; Editing by Ellen Wulfhorst, Barbara Goldberg, Eric Beech and Peter Cooney)