The amnesty “is a dramatic way to message to kids and young adults that we want you back, and we want you reading,” said Anthony W. Marx, the president of the New York Public Library. The forgiveness is not conditional on returning any overdue books or DVDs. “We want you to be responsible, but we don’t want to penalize you just because you are too poor to pay the fines.”

At the Hamilton Grange Library in Hamilton Heights, a Manhattan neighborhood where around half the school-aged card holders have their borrowing privilege suspended because of fines, Venice Beckford, 36, a child care provider, rejoiced at the news.

All three of her children — Amelia, 3, Makayla, 12, and Rohan, 16 — have had their library borrowing privileges suspended. She estimates that they owe at least $180 in unreturned book fees and fines.

Ms. Beckford said that between her family and work, she and her husband often forget to remind the children to return their books. But her house is filled with readers, she said. “We have books everywhere in our house.”

The one-time amnesty will be brief: Fines for new late materials will start accruing again the same day. It also does not apply to adult card holders. Dennis M. Walcott, the president of the Queens Library system, described the move as a necessary “experiment” that may help determine if a fine-free future is possible.