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.
Sporting director Nasco Syrakov and chairman Ivo Tonev have both offered their resignations following the controversy.
Batkov was quick to voice his anger at the chaotic scenes and express his support for Petev.
"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."
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