"So far, she's not said anything," said NYPD's chief of department, Kenneth Corey.
The search for the children intensified after the mother was found alone. Police sent in a helicopter and marine units. The children were found at the water's edge shortly after 4:30am on a quiet section of beach, about 13 blocks from the stadium where the Brooklyn Cyclones minor league baseball team play their games.
Efforts to revive the children at a nearby hospital failed, Corey said.
Police didn't immediately identify the children or the 30-year-old mother. A decision hadn't been made about what criminal charges she might face.
The children's bodies were found just three blocks from the woman's apartment building, where police had first gone when the search began. Corey said officers had canvassed the beach and the boardwalk, searched neighbourhood streets, and checked the local hospital in the hunt for the children, before the mother was found on the boardwalk.
Corey said the mother had not been reported to authorities previously for abusing or neglecting her children.
Family told the New York Post that the woman had been "struggling".
"We're devastated. They were kids. They were adorable kids," said her aunt.
"It's someone who was struggling, and no-one knew how bad the struggle was.
"In this family we do have a history of mental illness to varying degrees. A few of us have battled with bipolar disorder, but I didn't know her mental struggles. I just knew she was trying to find a way for her children, a way to get on her feet," she told the Post.
"She loved her children. She loved her children very much. It was the mental issues that took over."
SUICIDE AND DEPRESSION
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO (available 24/7))
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• What's Up: 0800 942 8787 (11am to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• Helpline: 1737
If it is an emergency and you feel like you or someone else is at risk, call 111.
- Additional reporting, NZ Herald