"No matter what religion we belong to, we must not close our eyes and hearts to the genocide in Iraq," it said in a press release on Thursday.
Islamic State (IS) militants have seized Qaraqosh, Iraq's biggest Christian town, prompting members of the Yazidi community to flee.
Officials have warned the Yazidis face starvation and dehydration if they remain stranded on Mount Sinjar, and will be killed by the militants if they move.
Iraq is home to one of the world's most ancient Christian communities, but numbers have dwindled amid growing sectarian violence since the US-led invasion in 2003.
The TKG press release warned of "a massacre amounting to a terrible genocide that is being carried out by a criminal Sunni Muslim group… under the guise of Islam.”
"The IS terrorists have nothing to do with the true Islam! They are murderers and criminals! These crimes must be internationally outlawed and punished," it continued.
The TKG is worried that some people will tar all Muslims with the same brush as the IS, and stressed that it was important to understand the differences between “the fundamentalists and racists who abuse Islam, and on the other hand peaceful and moderate Muslims."
The march will take place on Sunday August 10th at 4.30pm, meeting in front of the State Opera and walking from there to St Stephen's Cathedral.
The TKG said that it believes in "the possibility of peaceful coexistence in a community in which we share peaceful ideas and make new friends, regardless of race, religion and social status."