A London judge is hopeful Madonna and Guy Ritchie will find an "amicable settlement" in their ongoing international custody battle.

The stars have been fighting over who their son Rocco should live with after the 15-year-old refused to return to his mother in New York following a visit with his London-based father in December (15).

Madonna subsequently filed legal papers in both the Big Apple and the British capital, where she accused Ritchie of effectively kidnapping the teenager by allowing the kid to stay - against her wishes.

The case was heard in Manhattan Supreme Court on Wednesday (02Mar16), when Justice Deborah Kaplan scolded Madonna and her ex-husband, who both phoned in for the hearing, for dragging out the dispute in court instead of working together to find the best solution for their son.

She decided against ordering Rocco to return to New York and instead gave the warring exes until 1 June (16) to try and resolve the case amicably.

A preliminary hearing was held in London's High Court on Thursday (03Mar16), attended solely by Ritchie, and during the proceedings, Justice Alistair MacDonald concurred.

"It is highly unfortunate and deeply regrettable as Judge Kaplan said that this family dispute is being dealt with in front of her and in front of me, through the agencies of highly capable lawyers," Justice MacDonald told the court. "It is hoped further discussions between the parties can reach an amicable settlement."

Another hearing is set for later this month (Mar16), but lawyers for Madonna are reportedly seeking to withdraw her legal challenge from the High Court and end the proceedings in the U.K., according to Telegraph.co.uk.

Madonna and Ritchie previously agreed to have the singer raise Rocco in New York as part of their divorce settlement in 2008. The stars were married for eight years, during which they also adopted 10-year-old David Banda.

The Material Girl superstar, who is in the midst of her Rebel Heart World Tour, is also mum to daughters Lourdes Leon, 19, and Mercy James, 10.

Ritchie lives in London with his wife Jacqui Ainsley, who he wed in July (15), and their young kids Rafael, Rivka and Levi.

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