Australian mother Sally Faulkner has asked estranged husband Ali el-Amien to drop Lebanese abduction charges against her in exchange for her renouncing all claims to custody and co-operating in getting a divorce.

Ms Faulkner and four members of a Channel Nine 60 Minutes crew were among a group of people arrested after an attempt to take Ms Faulkner’s two children off the streets of the capital, Beirut.

If Mr el-Amien agrees to drop the charges, Ms Faulkner will give up sole custody granted to her by the Family Court in Australia.

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Mr el-Amien has pressed charges. Photo: Channel Nine

The Australian Family Court ruling, granted on December 15, even allowed Australian police or agents appointed by Ms Faulkner to get her children back — but she did not register it in Lebanon.

Mr el-Amien got his own custody ruling from a religious court in Lebanon, but it is not clear when it was issued.

The ABC has been told the Lebanese judge does not view the recovery as a kidnapping, but rather as a mother trying to reunite with her children.

Ms Faulkner hopes for the right to see her children whenever she wants in Lebanon, Australia or a third country.

If Mr el-Amien agrees to drop charges against Ms Faulkner, she would likely be released on bail and it could reduce the severity of charges against all involved.

The child recovery team were paid directly by Ms Faulkner, who used money given to her by 60 Minutes, her Lebanese lawyer Ghassan Moghabghab said.

But Mr Moghabghab said “I don’t have any idea” if 60 Minutes paid Ms Faulkner intending for it to go towards the operation, or just for her story.

Ms Faulkner’s children. Photo: ABC/Supplied

The payment can not be confirmed independently and the claims have not been tested in court.

Mr Moghabghab said Ms Faulkner told a judge she regrets paying for the attempt.

Earlier, authorities said they had a signed statement from a member of the recovery team saying Nine paid $115,000 for the operation.

However, that statement is uncorroborated and cannot be confirmed.

Mr Moghabghab said Ms Faulkner was in the car when alleged operatives of Child Abduction Recovery International grabbed her son and daughter off a Beirut street and bundled them into the waiting car.

“Maybe she was showing the persons that were executing [the abduction] who are the children, maybe they don’t know,” he said.

“Maybe she was present that if the children were taken from the grandmother, they began crying, so the presence of the mother, it will be easier for them to take the children and give them to their mother.”

The team made a clean getaway, but was caught not long after the fact. Soon after, the boy and girl were returned to the father and Ms Faulkner and the 60 Minutes crew were arrested.

-ABC