Ritchie attended a hearing before judge Alistair MacDonald. Neither Madonna nor 15-year-old Rocco was present.
Madonna wants Rocco, who lives with his filmmaker father in England, to return to her custody in the U.S.
The case has unfolded in New York, but Madonna also issued an application in England under an international legal convention. Lawyers say the singer now wants to withdraw it and end the British legal proceedings.
On Wednesday, a New York judge implored the couple to put their son's interests first and end their months-long legal battle. Justice MacDonald echoed that sentiment, saying it was his 'fervent hope' that the couple could reach an agreement.
'An amicable negotiated resolution is definitely the way forward and in Rocco's best interests,' he said.
Another hearing is scheduled later his month.
In December, New York State Supreme Court Justice Deborah Kaplan ruled that Rocco should return to his mother's custody. Records show Madonna, whose legal name is Madonna Louise Ciccone, moved for the judge to enforce that order.
On Wednesday, Kaplan said she wasn't going to remove the order but also would not issue a warrant to compel Ritchie to appear in New York.
From Associated Press Via Yahoo! News