Shocking footage of the singer hitting the rapper - who is her brother in law - after the Met Ball in New York surfaced last week, but the pair say they have since put the incident behind them.
A joint statement from Solange, Jay Z and his wife Beyonce - who was also in the elevator at the time - read: ''As a result of the public release of the elevator security footage from Monday, May 5th, there has been a great deal of speculation about what triggered the unfortunate incident.
''But the most important thing is that our family has worked through it. Jay and Solange each assume their share of responsibility for what has occurred.
''They both acknowledge their role in this private matter that has played out in the public. They both have apologised to each other and we have moved forward as a united family.''
In the soundless video, Solange can be seen lashing out with punches and kicks at '99 Problems' star Jay, before she is pulled off by a security guard.
The statement continued: ''The reports of Solange being intoxicated or displaying erratic behavior throughout that evening are simply false.
''At the end of the day families have problems and we're no different. We love each other and above all we are family. We've put this behind us and hope everyone else will do the same.''
New York's Standard Hotel, where the incident took place said it had fired the person who leaked the video yesterday (14.05.14).
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