IAN McLeod, the Celtic chief executive, has written to supporters urging them not to chant IRA slogans at matches.
The call comes after discussions with the club's supporters' associations and the Celtic Trust.
A minority of Celtic fans disrupted the one minute's silence for the victims of the September 11 atrocities last week before the start of the match at Motherwell.
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Neil Lennon, the Celtic midfielder, was also the victim of sectarianism last month when he was forced to withdraw from the Northern Ireland side after a death threat.
Mr McLeod insists the roots of the club are founded on the principle of being open to all.
He said in his letter to supporters: ''There are . . . some who appear to criticise Celtic for encouraging those from other backgrounds or national identities to become part of the Celtic family, as they perceive such encouragement as some attempt to dilute the importance of our background and origins.
''This is not the case. Celtic is a club for everyone and open to all. We anticipate that our supporters would regard such an approach as a positive one.
''We are a Scottish club, proud of our Irish roots, but our words need to be backed up by the actions we take, particularly in relation to politics.
''It is therefore a concern that a limited but vocal number within our support seek to use the gathering of Celtic supporters as a way of demonstrating their own separate support for organisations at the extreme of the political spectrum; most notably the IRA.''
Mr McLeod went on to condemn the actions of a ''vocal minority'' for besmirching the name of the club.
He continued: ''We are a football club first and foremost and clearly it is not our position to dictate to anyone what political beliefs or actions should or should not be.
''However, it is equally our responsibility to ensure that the club - as a non-political organisation - retains its political independence by appealing to those who participate in such activities in the name of Celtic Football Club to stop doing so.
''This promotion of the IRA is most obvious among a section of our away support and was clearly audible at our game against Motherwell during the minute of silence in memory of the victims of September 11 while supporters were still entering the ground.
''This action by a minority will lead to criticism of Celtic Football Club and indeed has led to calls to Celtic Park (not for the first time) from Celtic supporters who do not share these political beliefs but find themselves linked to them by association.
''I am therefore appealing to those who are allocated tickets and those who attend games not to participate in or condone such activities in order that Celtic is not compromised in the future.''
Donald Gorrie MSP, a long-time campaigner against sectarianism, said: ''It is appropriate that Celtic is calling for supporters to ensure they do not condone the chanting of sectarian songs. It is time for other clubs to write to fans to get across the message they do not condone the shameful actions of a minority.''