Madonna wants to heal the family wounds caused by a dispute with her ex-husband over custody of their son Rocco, her lawyers told the High Court.
The US pop megastar's lawyer told judge Alistair MacDonald that she wanted to end the court battle being fought in London with British film director Guy Ritchie over their 15-year-old son.
They are also engaged in similar court action in New York.
MacDonald finished hearing evidence on Friday and now has to decide whether the High Court proceedings should close, or if he should make decisions about Rocco's welfare.
A New York judge in December asked Ritchie to send Rocco back to the US, after he decided to move to London rather than stay in his mother's home or accompany her on tour.
Ritchie has attended the London court hearings, though Madonna has been singing in Australia and New Zealand.
"What she has always wanted 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," said Madonna's lawyer David Williams.
The singer wants 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, adding that Madonna wants them to meet in New York over Easter.
Ritchie's lawyer, Alex Verdan, said the director had proposed a meeting in London as the pair had not been in the "same place at the same time"since the dispute began.
The couple split in 2008 after eight years of marriage.