Updated

The parents of two children prosecutors say were stabbed to death by their nanny in a shocking 2012 killing that haunted the city are asking the public to try to think positive as the criminal case finally goes to trial.

Kevin and Marina Krim said in a video message Friday the trial will be inevitably difficult. The family's nanny, Yoselyn Ortega, has pleaded not guilty to murder in the deaths of 6-year-old Lulu and 1-year-old Leo.

Jury selection is underway; her lawyer unsuccessfully challenged a judge's ruling that she is mentally fit for trial.

The Oct. 25, 2012, killing stunned the city, where tens of thousands of nannies are employed by parents who entrust them with their children. Reports of serious violence by caregivers against children are exceedingly rare.

On the day of the killings, Marina Krim left to go pick up her third child, Nessie, from a swimming lesson. She returned home to their darkened apartment and discovered the others in the bathtub. The nanny was found on the bathroom floor with self-inflicted stab wounds to her neck, prosecutors said.

"Over the next few months, the story of Lulu and Leo and our whole family will be painfully in the news again," Kevin Krim said in the video message, shot as Nessie and their two younger children, Felix and Linus, played behind them in their apartment. "This trial will be very hard for us, and for a lot of you. We feel like this community ... all of you ... have been with us all along, through this whole experience."

The couple asked anyone concerned for them to spread the word about the family's nonprofit, the Lulu & Leo fund, which supports creative education in schools.

"We thought about it, and we realized that we're going to handle this the way we've handled everything," said Marina Krim, who is expected to testify in the upcoming trial. "We're going to focus on the positive and the goodness that has come out of all of this."

She asked that when the family is on the news, or comes up in conversation as the trial progresses that people instead talk about their nonprofit and the work it's doing to help give children time to be creative.

"This is the legacy of Lulu and Leo, and this is what matters, so this is how you can help us," Marina Krim said.

The kids then help detail the nonprofit's mission.

"It was inspired by my sister and brother Lulu and Leo, they loved being creative," Nessie said.

The trial is expected to last several months. According to court papers, Ortega told authorities the little girl tried to fight back before she stabbed her and then killed the boy. She used at least two knives, she said.

"Oh, my God, I'm sorry. I'm sorry for what I've done," she said, according to the court papers. "Relieve me of my misery."

Her attorney has argued she is mentally ill.