In a statement issued ahead of Tuesday night's Championship clash with Charlton, the West Yorkshire club called for fans who hear "sick chants" to "turn their backs on the game".
Both Leeds and Wednesday fans have attracted criticism over the course of the last four days after exchanging unsavoury songs at Hillsborough.
Sections of the Leeds support taunted Wednesday boss Dave Jones about child abuse charges he was cleared of in 2000, as well as heralding the life of the now-disgraced broadcaster Jimmy Savile, while home supporters sung about the two Leeds fans murdered in Turkey in April 2000.
Tempers on the terraces flared further when Leeds fan Aaron Cawley ran on to the field and attacked Wednesday goalkeeper Chris Kirkland. He was jailed on Monday.
In launching the initiative, Leeds chief executive Shaun Harvey said: "In an age when so much has been done to improve the game's image it is sickening that these vile chants can still be heard in and around stadiums up and down the country.
"Our fans have been the perpetrators and the victims of vile and sick chants, particularly with reference to the two fans who lost their lives in Istanbul 12 years ago. We don't believe there is any place for this in football.
"We are asking our fans to show their feeling towards any vile chants they may hear by turning their backs in response, rather than react in any other way."
The requesting of fans to turn around is a poignant one for Leeds, for that is what they did to mark the 10-year anniversary of the deaths of Christopher Loftus and Kevin Speight - the men who died in Istanbul - at an away game with Yeovil in 2010.
However, despite the club's actions, chairman Ken Bates believes the events of Friday night could have hindered the ongoing takeover negotiations with Bahraini investment company GFH Capital.
The two parties have been in talks since May, and Bates tonight confirmed that GFH had made an upfront payment of £2million. A deal remains off the table at the moment, though, and Bates said: "What message does that (Friday) give to potential investors and commercial partners?
"I don't know what they (GFH) must be thinking after watching Friday night's events unfold."
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