A lawyer for the singer told Mr Justice MacDonald that she wanted to end litigation.
Her hopes for the future were revealed at a private hearing in the Family Division of the High Court in London on Friday.
The singer and the film-maker are embroiled in litigation in England and New York.
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.
Lawyers have told Mr Justice MacDonald that Madonna wants to end legal proceedings she had launched in England.
The judge has to decide whether English proceedings should draw to a close or whether he should make decisions about Rocco's welfare.
He finished hearing evidence on Friday, after a hearing lasting several days, and is expected to deliver a ruling in the near future.
Rocco and Mr Ritchie had been at the hearing but not Madonna. The singer's lawyers told the judge that she wanted to attend but was on tour in Australia.
Mr Justice MacDonald urged Madonna and Mr Ritchie to try to settle their dispute. And lawyers told him that both Madonna and Mr Ritchie had outlined proposals for negotiation.
Madonna proposed that Rocco and Mr Ritchie travel to her home in New York when she ended her current tour to try to 'reach a resolution'. Mr Ritchie proposed a 'round table' meeting in London involving lawyers.
Members of Madonna's legal team had taken instructions from her after she finished performing in Melbourne on Thursday. And David Williams QC, who headed the team, outlined Madonna's wishes on Friday.
'What she has always wanted to do and still continues to seek to do is to find a way in which this family can get to heal the wounds which have been inflicted on this family over the past four months or so and to chart a course for Rocco and the family which enables them to put this behind them and to restore peace to the family,' he said.
'She really very much hopes that the family can get back together in New York over the Easter vacation and start the process, with all of them involved, in trying to reach a resolution to this problem.'
Alex Verdan QC, who represented Mr Ritchie, said his client had proposed a round-table meeting in London. Mr Verdan said any lawyers anyone wanted would be able to attend.
He said Madonna and Mr Ritchie had not been in the 'same place at the same time' since the dispute began.
Mr Justice MacDonald said one of the problems was that Madonna and Mr Ritchie, a film-maker, could not decide which country negotiations should take place in.
The judge had ruled earlier this week that little detail could be revealed about the hearing in London. But he relaxed restrictions on Friday after an application from the publishers of The Sun and Daily Mail newspapers.
From Associated Press Via Yahoo! News