Assem al-Gohary, assistant justice minister for the Illicit Gains Committee, has said in a statement that business tycoon Hussein Salem and his son Khaled filed an appeal on Thursday against a ruling by the Spanish Supreme Court to hand them over to Egypt.
His daughter Magda, whom the court also decided to extradite to Egypt, did not challenge the ruling.
Salem left Egypt a week before Mubarak was forced to resign in February 2011.
Egyptian protesters have pressed for the prosecution of Mubarak and his cronies due to years of alleged abuse and corruption.
Last week, Spain's National Court announced it had ordered Salem to be extradited to Egypt along with his son.
Salem, an ex-army and intelligence officer, had been closely linked to Mubarak since the early days of Mubarak's regime three decades ago.
The Spanish court conditioned that they are not to be sentenced to death in Egypt and that they must be tried before a court other than the one that had issued the charges against them.
Salem and his children are charged with several crimes, including money laundering in collaboration with the former president.
Investigators froze US$47 million in accounts held by Salem and police also seized homes worth $14 million, including seven in the southern Spain jet-set resort of Marbella.
Salem is alleged to have won lucrative land and other deals, including exporting gas to Israel, because of his close connections to Mubarak. The natural gas deal has been heavily criticized in Egypt.