In its report published yesterday, the group branded the sport's efforts to tackle the problem in football as "tokenistic and superficial."
The Advisory Group on Tackling Sectarianism was set up 16 months ago.
At the launch of its paper on religious bigotry in Scotland the group's head, Dr Duncan Morrow, said despite the absence of the clubs for that time, he still intended to meet them.
One source said: "Put it this way, there was some difficulty coordinating diaries between Celtic, Rangers and the group over nearly a year-and-a-half."
The Scottish Government will also carry out two national surveys on bigotry, one looking at public attitudes to sectarianism, and one to include in-depth qualitative research on community experiences of the problem in Scotland.
The advisory group, which met over 40 organisations, will now remain in place until March 2015.
The Herald revealed yesterday that the group had concluded sectarianism neither stemmed from nor was the responsibility of denominational schooling.
It said local government should get to grips with community rights around parades, and Scotland needed no new laws to deal with the problem.
However, it has body-swerved the issue of the controversial Offence Behaviour at Football Act, citing an expected review of the legislation.
The report said Scottish sectarianism was not merely religious but something which "can involve a negative mixing of religion with politics, sporting allegiance and national identifications … arising from a distorted view of identity and belonging".
Sectarianism, the authors add, does not have to be "explicitly contemptuous, aggressive or offensive, can be polite and educated and may populate boardrooms, trustee committees, professional bodies, schools and government".
Ingredients often include anti-Irish and anti-British hostility related to Irish politics, historic elements of anti-Catholicism, class and political affiliation, and commercial interests.
Concern was also expressed at the "apparent reluctance of many senior and influential people across Scottish society to show the kind of leadership required to tackle sectarianism".
The report calls for "leadership to challenge the environment of friendly indulgence or passive acceptance of sectarian 'banter'".
On football it states: "It is impossible to ignore the fact that sectarianism continues to exist at many levels in Scottish football.
"We need to go beyond tokenistic and superficial gestures to deeply embed an anti-sectarian ethos into, and across, every area."
Dr Morrow said: "Sectarianism is real in many communities and this is a long game. It has withered in some places, and remains intact or has mutated in others.
"It is a subtle issue which we hope will become something talked about in the history classes of the future. There is good news in this. It doesn't appear to be the burning issue for the whole of Scotland that it may have been once.
"And just about everyone said it wasn't a positive in Scottish life."
Announcing the two new national surveys, community safety minister Roseanna Cunningham said: "We have got historic studies on sectarianism but nothing underpinning the current scenario.
"We don't want policy based on anecdote. Perception and experience isn't always the same."
A Celtic spokeswoman said: "The continual inference that football in some way is responsible for sectarianism does not understand or reflect the wider issue.
"Sectarianism is a symptom of social failings and is therefore a matter for society as a whole."
A Rangers spokeswoman said: "We have also indicated to the advisory group that we are happy to offer them any assistance ."
She added: "Rangers and other … clubs have shown leadership on the subject and our initiatives have been effective and ground-breaking."