Mr Justice MacDonald said it would be a “tragedy” if any more of the “fast-receding days” of the teenager’s childhood were taken up by the dispute.
The judge said Rocco was a “very great credit” to his parents. He said it would be better if Madonna and Mr Ritchie could each enjoy his company.
The dispute relates to where the teenager should live. Judges have heard that Rocco had remained in London with his father, after a visit. Madonna wants the teenager to return to live with her, in the US.
Litigation had begun in London and the US. Mr Justice MacDonald made his plea for peace after ruling that the English proceedings could be halted.
The judge analysed the latest round of the dispute, at a private hearing in the family division of the High Court, in London, earlier this month.
He was asked to decide whether he should allow English proceedings to draw to a close — or whether he should make decisions about Rocco’s welfare. More court hearings are expected to be held in New York.
No-one involved was in court when Mr Justice MacDonald handed down his ruling on the future of the case in England.
“At the root of these proceedings ... is a temporary breakdown in trust,” said the judge. “For all the media coverage, comment, and analysis, this is a case born out of circumstances that arise for countless separated parents the world over.
“I renew, one final time, my plea for the parents to seek, and to find, an amicable resolution to the dispute between them. Because agreement is not possible today does not mean that agreement will not be possible tomorrow.”
A judge in New York has made similar pleas.
Lawyers have told him that both had outlined proposals for negotiation.
Justice MacDonald said Madonna had issued proceedings under international legislation, relating to parental disputes about children, in London on December 21.
She made an application, under the 1980 Hague Convention, for the summary return of Rocco to the jurisdiction of the US, specifically to New York state.
The judge said two days later Madonna launched separate proceedings in the Supreme Court of the State of New York.
Mr Justice MacDonald said Madonna and Mr Ritchie married in December, 2000, and divorced nine years later.
They agreed that Rocco would live in the US with Madonna, but spend time with Mr Ritchie.
A family court judge approved that agreement.
In November 2015, arrangements had been made for the Christmas period.
Rocco was due to return from his father, in London, to his mother, in New York, in early December.
However, he did not return and remained in the care of Mr Ritchie, said the judge.