The company demanded a retrial after claiming the previous judge's "misconduct" was "profound".
In a legal brief, which attacked each of the arguments made by the Department of Justice (DoJ), Microsoft claimed that district court judge Thomas Penfield Jackson's "misconduct" was "so profound that it is difficult to imagine a case in which a new trial would be more appropriate".
The DoJ recently indicated that it no longer wanted to break Microsoft into two separate companies - the original solution that had been supported by Jackson, who was removed from the case after discussing his findings with journalists before speaking to the court.
Microsoft argued to the Supreme Court that the Appeals Court did not go far enough in throwing out Jackson's remedy. The company said the Appeals Court should have thrown out his entire verdict and ordered a retrial.
Meanwhile, district court judge Colleen Kollar-Kotelly, who replaced Jackson last month, is due to meet Microsoft and the US government on 20 September to address outstanding issues. The hearing could shape the rest of the proceedings.
The Appeals Court has given Kollar-Kotelly the task of deciding certain questions of law and proposing a new solution.