The leaked recordings aired on pro-Mursi satellite channels on Friday, depicting a debate among senior military and security officials over forging trial evidence against Mursi before he was formally charged with multiple crimes under the civilian court system.
It allegedly features General Mamdouh Shahin, legal adviser to then army chief and now President Abdel Fattah al-Sisi, warning other senior officials in Sisi's office that the case against Mursi would collapse if documents were not forged.
Al Jazeera cannot independently verify the contents of the recordings.
The prosecutor general's office blamed the Muslim Brotherhood for fabricating the footage and telephone conversations "using advanced technology" with the aim of "causing disruption and destabilising society.''
In a statement, it vowed to fight such "crimes" and ordered an "extensive investigation to find those responsible."
Mursi has been in jail since he was overthrown last July and is on trial for inciting the killing of opposition protesters in December 2012 outside the presidential palace.
The deposed president also faces charges of espionage in collaboration with the Palestinian movement Hamas.
The Egyptian government has repeatedly said Mursi's toppling was not a "coup", but a decision taken after mass street protests rocked Cairo and other cities on June 30, 2013.