The two children were allegedly snatched off a Beirut street earlier this month at their mother's behest.
The operation was being filmed by four Australian journalists with Channel 9's 60 Minutes programme.
The mother, Sally Faulkner, was soon arrested, as were the journalists, two British men and two Lebanese men.
The children were returned to their father's custody.
The judge overseeing the case has warned that he views the "child recovery" operation as a criminal case.
Ms Faulkner had said she had not seen the young children since her estranged husband, Ali Elamine, took them from Australia to Beirut on holiday.
She flew to Lebanon earlier this month with two employees of the UK-based company Child Abduction Recovery International (CARI) to recover them, accompanied by the 60 Minutes team.
CCTV footage broadcast by Lebanese TV appears to show the six-year-old and four-year-old being bundled into a car by several men on a busy street in southern Beirut.
They had been heading to school with a domestic worker and their paternal grandmother, who said she was knocked to the ground during the abduction.
It was previously reported that the judge was pushing for Ms Faulkner to reach a custody agreement with Mr Elamine.
But Mr Elamine has now said he will not drop abduction charges against Ms Faulkner because it could see the others involved released as well.
Judge Rami Abdullah said on Monday that the so-called "recovery" operation amounted to a kidnapping attempt.
"This is not a custody case, they are involved in kidnapping two kids," he said, according to News Corp Australia.
The case has been adjourned until Wednesday to allow both sides to negotiate.
Those arrested face kidnapping, assault and association charges, which can carry a sentence of up to 10 years in jail.
According to reports, Judge Abdullah interviewed 60 Minutes' prominent reporter Tara Brown and Ms Faulkner briefly on Monday before the handcuffed pair were escorted out a side exit to waiting police cars.
Australia's Foreign Minister Julie Bishop has been in contact with her Lebanese counterpart.
"The law in Lebanon is quite different to Australian law," she said in an interview with Network Ten.
"It's based on a French system, so there have been arrests, then an investigation and then an investigating judge determines whether charges will be laid and I understand we're at that stage of the proceedings," Ms Bishop said.
Lebanon is not party to the Hague Convention, a treaty designed to ensure the swift return of children abducted internationally by a parent.
A Lebanese man whose estranged Australian wife has been charged with attempting to kidnap their children has said he will not drop the charges.