The Scottish Independence Convention (SIC), fronted by actress Elaine C Smith, has called on Alex Salmond to reject a "meaningless" second question.
The body added that offering voters more powers for Holyrood would make it difficult to produce an "unbiased" ballot and a "clear result".
The SNP won a landslide victory at last year's Holyrood election, with the promise of an independence referendum in their second term a central part of the campaign.
However, since being returned to government, Salmond has said he is open to devo max – effectively financial independence – also being on the referendum ballot. He dropped a bigger hint on the subject recently after he told a US audience that Scots had a "right" to a second question.
The First Minister believes public opinion is on his side, but opposition unionist parties say Salmond fears he cannot win a straight fight on independence. Latest opinion polls show that on a straight one-question referendum 50% oppose independence with 30% in favour. But when a second question is mooted support for independence falls to 23%, support for the union falls to 29%, while support for more powers – devo max – rises to 37%.
Aside from unionist criticism, the First Minister is also encountering hostility to a second question from the pro-independence camp.
Yes Scotland chief executive Blair Jenkins said he would campaign only for independence, while the same organisation's chairman, Dennis Canavan, said devo max was "completely confusing".
The Scottish Socialist Party, also in the pro-independence movement, is against devo max, while Green co-convener Patrick Harvie said the second option lacked "clarity".
It has now emerged the SIC, formed in 2005, is also determined that the referendum ballot should have one question. In a statement flagging up its response to the Scottish Government's consultation on the referendum, it stated: "The SIC is opposed to having two questions on the referendum ballot paper."
SIC vice-convener Kevin Williamson said there were "two important reasons for rejecting two questions", the first being that independence was "qualitatively different from devo-plus or devo-max".
He argued: "It [independence] will create a fundamentally new legal status for Scotland, forever after giving the Scottish people power to make their own choices and ensuring that we have an established place in the international community. This is a decision of a different order from being granted some additional powers from Westminster."
He also claimed that a second question threw up "issues of clarity of outcome", noting: "A second question would be meaningless unless it related to a very clearly defined constitutional scheme which was widely publicised and had the support of a major political party or substantial civic o rganisations. This seems unlikely to be the case."
Scottish Labour's constitution spokeswoman, Patricia Ferguson MSP, said of the split: "When members of the independence movement are saying this you have to wonder why the SNP are try to desperately to muddy the waters."
Scottish Liberal Democrat leader Willie Rennie MSP said: "It is clear that the SNP are facing considerable problems over their strategy."
A Scottish Government spokesman said, "Our policy is independence," but added: "We recognise there is substantial support - for increased responsibilities for the Scottish Parliament short of independence.
l More than 26,000 responses were received during the Scottish Government's consultation on an independence referendum. Analysis will be published at the end of the summer.
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