JERUSALEM (CNN) -- Israeli police divers found a suitcase Thursday containing human remains that are believed to be the body of a missing 4-year-old girl, an Israeli police spokesman said.
The suitcase was pulled out of the Yarkon River in Tel Aviv, where police have been searching for Rose Pizem, Mickey Rosenfeld said.
Two weeks ago, the girl's grandfather Roni Ron, 45, told police he stuffed her body in a suitcase and dumped it in the Yarkon River.
The remains will be tested to confirm the identification of the body, and the tests could be completed within 24 hours, Rosenfeld said.
"The body was found in a very bad, severe condition, as you can imagine after being in the water for weeks," Rosenfeld said, explaining why the tests could not be completed sooner.
Ron initially told police he accidentally killed Rose when he slapped her in a fit of rage but then changed his account.
Police transcripts quote Ron as saying, "I parked the car on the sidewalk. I opened the trunk, pulled out the suitcase and when I reached the banks of the river, I threw it. She's finished. I finished her. I saw the water seeping in and the suitcase slowly sinking."
The family drama centers on Rose's mother, Marie-Charlotte Renault-Pizam, 23, and Ron -- her estranged husband's father -- with whom authorities say she has had two more daughters. Rose's father lives in France.
Both the mother and grandfather are in custody.
Renault-Pizam has denied any role in her daughter's disappearance. She told police she thought Ron sent Rose to an institution in France, although police, without elaborating, have said they have a telephone conversation that shows she knew the child's fate.
Rose's great-grandmother, Vivienne Yaakov, reported the girl missing in late July, saying she had not seen her great-grandchild for about two months. Rose and her mother had been staying with Yaakov, who told police that Ron had taken the child and she never returned.
Police searched Ron's apartment in mid-August and arrested him.
The investigation has uncovered a twisted family love triangle that may have contributed to the girl's murder.
The British media call the case Israel's Madeleine McCann, a reference to the 3-year-old child who disappeared May 3, 2007, while on vacation with her British family at the Portuguese resort of Praia da Luz. She has never been found.
Rose was born in France in 2003. Her mother moved to Israel after a custody battle with Rose's father, Benjamin Pizem. Renault-Pizam had fallen in love with Ron on a previous trip to Israel with her father-in-law.
Israel's minister of interior security, Avi Dichter, said everything would be done to find Rose and give her a proper burial.
"There is no doubt that as a society, Israel was not there for the child when she was in need of help," Dichter said.
Benjamin Pizem told Israel's Haaretz newspaper that he still hopes Rose is alive. He described his father, from whom he is estranged, as manipulative and said more details may be uncovered.
"When I see him in videos, I see in his face, even if it's quite a neutral one, he has an expression that says, 'You don't know everything, and I'm manipulating all of you.' That's the reason why we think there's hope Rose is still alive."