Petev was appointed by Levski following the departure of Slavisa Jokanovic, who was sacked on the back of a mediocre start to the campaign.
However, Petev - winner of consecutive A Football Group titles with league leaders Ludogorets - saw his appointment met with furore by some fans, who believe he is a supporter of Levski's fierce rivals CSKA Sofia.
A group of Levski followers interrupted his opening press conference, removing Petev's club shirt before ushering the 38-year-old to the exit.
"What happened today (Tuesday) is a disgrace. The case is unprecedented," Batkov said in a statement on the club's official website.
"Our ancestors who created this club would never have thought that this could happen. This is a stain on the club.
"Syrakov and Tonev have offered to resign. In the coming days we will decide whether to accept.
"The appointment was a decision we came to collectively.
"Petev is one of the few specialists who has proven that they know football, and we will not retreat."
