WELLINGTON, New Zealand — A rift emerged Monday between New Zealand’s government and the Red Cross over the humanitarian organization’s decision to name a New Zealand nurse who was kidnapped by the Islamic State five years ago — and who her employer believes could still be alive.

The divide was another twist in the unusual story of the lengthy captivity of Louisa Akavi, which was kept secret for years by a government and an employer initially in lock step about the need to stop it from becoming public. If she is still alive, she would be the longest-held hostage in the 156-year history of the International Committee of the Red Cross.

Ms. Akavi, 62, is a nurse and midwife who was abducted in late 2013 in the northwest Syrian city of Idlib along with two Red Cross drivers who are Syrian nationals. She was most recently sighted, according to Red Cross officials, in December at a clinic in Sousa, one of the final villages held by the Islamic State.

The Red Cross said it had named Ms. Akavi with the New Zealand government’s support in hopes of receiving information that could lead to her safe return. The timing was now right, the group said, after the Islamic State lost its last shred of territory in Syria last month.