A nanny accused of killing two children under her care in their Manhattan apartment turned down an offer from a judge on Thursday that would have given her a prison sentence of 30 years to life in return for guilty pleas to both murders.

Justice Gregory Carro told the nanny, Yoselyn Ortega, 53, in State Supreme Court in Manhattan that he would be willing to sentence her to 15 years to life for each murder, with the terms to be served consecutively, if she took responsibility for her acts.

But Ms. Ortega’s lawyer, Valerie Van Leer-Greenberg, said her client “doesn’t want to accept this offer at this time.” She said she had discussed the judge’s offer, which had not been made public, several times with her client over the last three months.

A prosecutor, Stuart Silberg, said the Manhattan district attorney’s office did not agree with Justice Carro’s offer. “The people believe the only appropriate sentence is life without parole,” Mr. Silberg said. “The family doesn’t want that to be the disposition.”