Only half of people who support independence are strongly in favour of it, a poll has suggested.
The YouGov survey commissioned by the pro-union Better Together campaign found that 31% of people favour independence, with 16% strongly supporting it and 15% who "tend to support it".
Of the 56% the poll found to be opposed to independence, 37% were strongly against it.
The study of 1011 people was carried out two days after the First Minister and the Prime Minister signed the referendum agreement in Edinburgh.
It shows that there is support for independence from people who identify themselves with other political parties than the SNP.
When asked about their voting intentions for Westminster, 5% of people surveyed who supported the Conservatives also back independence, while 21% of Labour supporters and 17% of Liberal Democrat voters are also in favour.
The poll found that 11% of people who intend to vote for the SNP at Westminster are opposed to independence.
Blair McDougall, Better Together's campaign director, said: "This poll reveals a deep lack of confidence, even amongst instinctive supporters of independence, in the proposition of breaking up the UK.
"The longer the SNP put off answering the most basic of questions on independence the more people will lose confidence in leaving the UK.
"Would the EU demand Scotland sign up the euro? Would we have to agree our public spending limits with London?
"What would the cost of borrowing be for Scotland? These are not questions that can wait to be answered in a few paragraphs of a White Paper next year."
A spokesman for Yes Scotland, the cross-party pro-independence campaign, said: "This poll clearly shows that people of different political colours support independence and as a broad church movement we very much welcome that.
"The historic Edinburgh Agreement signed this week marks only the beginning of the independence debate.
"People in Scotland are seeking information and over the next two years we are confident that, as the choices become clearer, the economic and social benefits of an independent Scotland will lead to a yes vote in 2014.
"Independence is about taking responsibility for making our own decisions according to our own values, priorities and aspirations.
"An independent Scotland will usher in a new social union that will strengthen our friendship and relationship with the rest of the UK."
More About Referendum
- Teenager stole saltire flags and referendum placard from gardens
- Scots would vote Yes if referendum was held now, according to poll
- New voter registration system must be 'carefully implemented'
- Alex Salmond hints at second referendum if devolution 'Vow' not kept
- Lord Smith warns parties against backsliding on more powers
- Referendum uncertainty led to housing market drop, says survey
- Sturgeon: Scottish independence is a matter of 'when, not if'