By Natasja Sheriff

NEW YORK (Reuters) - A New York jury ended its 16th day of deliberations on Wednesday with no verdict in the murder trial of a former deli worker who confessed to the 1979 killing of Etan Patz, a 6-year-old whose disappearance changed the way the United States responds to reports of missing children.

The jury has been struggling to weigh kidnapping and murder charges against Pedro Hernandez, 54. The panel in state Supreme Court in Manhattan has twice told Judge Maxwell Wiley it was deadlocked but both times was ordered to keep trying.

Jurors were due back in court on Thursday to begin a 17th day of deliberations.

Hernandez told police in 2012 that he choked the boy in the basement of a deli where he worked, stuffed him in a box and left his still-moving body in an alley. Hernandez's attorneys argued he is mentally ill and that police coerced his confession.

Patz vanished on May 25, 1979, while walking alone for the first time to the school bus stop in his Soho neighborhood in Manhattan.

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

There is no limit to the number of times a judge could order a deadlocked jury to keep trying to reach a verdict, but at some point such instructions would be considered coercive by an appeals court, said Alice Fontier, one of the defense attorneys.

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.

The defense says Hernandez is innocent and instead 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.

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.

(Editing by Barbara Goldberg, Will Dunham and Cynthia Osterman)