Sir Alex Ferguson has called for Manchester United and Liverpool fans to end the tasteless chanting that has marred games between the two clubs.
Liverpool have had to endure chants from their rivals' supporters about the Hillsborough disaster.
But Liverpool fans have also been guilty of singing about Manchester United's Munich air disaster.
"You'd hope that this is a line in the sand in terms of how the fans behave with one another," Ferguson said.
The Scot, speaking at a news conference ahead of United's home game with Wigan on Saturday, added: "We are two great clubs and we should understand each other's problems in the past. Certainly the reputation of both clubs doesn't deserve it.
"Both clubs have suffered fatalities through football.
"You hope that fans do behave themselves and support their team and that will be the end of it."
Ferguson's remarks come after a damning report of the Hillsborough Independent Panel cleared Liverpool supporters of any blame relating to the 1989 tragedy, when 96 fans died, and revealed South Yorkshire Police changed statements.
Prime Minister David Cameron on Wednesday offered a "profound" apology to the families of those who died.
Liverpool and Manchester United meet at Anfield in the Premier League on Sunday, 23 September.
It will be Liverpool's first home game since the dramatic findings relating to the Hillsborough disaster were released.
"The fact we are playing them after the findings we have been reading about in the last couple of days does bring a focus to it," Ferguson added.
On Thursday, Liverpool manager Brendan Rodgers said he hoped the publication of the truth about the Hillsborough disaster would end the hurtful chants by "idiots".
"I speak as a human being and I don't ever like to hear anything like that, whatever club it is, that associates with other people's tragedies and death," Rodgers said.
"Unfortunately you have a very small percentage of idiots at any club who will always try to smear another club's reputation."
Meanwhile, United midfielder Darren Fletcher returns to the squad for the visit of Wigan after 10 months out with a serious bowel problem.
"Darren Fletcher is in the squad," Ferguson said. "At this moment in time everything looks fine."