The centre-right "Narod i Pravda" party, which is part of the ruling coalition in the Sarajevo canton, said it feared the parade would "deteriorate the security situation" in the capital.
"Any escalation of the already boiling political situation can have negative consequences," the party warned.
The leader of the regional government, however, responded Friday saying that march was approved by authorities and that it was their "duty" to ensure it unfolded in a "dignified and clam manner".
"I will do everything in my power to ensure that all its citizens are treated equally, that they have freedom of assembly and police protection," regional Prime Minister Edin Forto, who hails from a liberal, multi-ethnic party, said in a statement.
Since October 2018 elections the canton of Sarajevo has been governed an ideologically mixed coalition that came together to end years of majority rule by the main Bosnian Muslim party, the SDA.
Some 1,250 police officers are expected to be deployed to the parade, according to a police source who requested anonymity.
The organisers expect between 500 and 1,000 people to join the march, including several foreign ambassadors and members of the European Parliament.
Sarajevo is the last capital in the Western Balkans to hold a Pride march.
While many welcomed the plans, the conservative SDA party also condemned the event after it was announced in April.
An elected representative from the party wrote on social media that she wanted "such people to be isolated and put as far away from our children and our society as possible".
The comments were condemned by the Council of Europe and deleted by Facebook after they were deemed "hate speech".
Discrimination is illegal under Bosnia law, but same-sex marriages are not recognised and, like much of the Balkan region, there is a strong strain of intolerance for the LGBT community.
Around half of Bosnia's population practices a moderate form of Islam, while another third are Orthodox Christian Serbs and 15 percent are Catholic Croats.
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