Makaziwe and Zenani Mandela are fighting a 2004 court order that gave Nelson Mandela the right to instruct his then lawyer, Ismail Ayob, to stop managing his financial affairs.
Ayob is now representing the daughters, The Star reported.
The suit, which was filed last week in Johannesburg, comes after the sisters asked the court last month to remove two trustees and directors of the Mandela Trust.
Mandela's lawyer, Bally Chuene, said the problem began in 2011 when executors of the ex-president's trust refused to release the money to his daughters.
"It is plain that Makaziwe and Zenani and Ayob had set about a general plan to have all of Mr. Mandela's independent trustees removed from their office in these trusts in order to gain control thereof," Chuene said.