Alex Salmond is preparing to stage a referendum on Scottish independence that will offer voters a second option – full financial autonomy while remaining part of the United Kingdom.

In an exclusive interview with the Guardian, the first minister said that allowing Scotland to have fiscal autonomy without full independence was "a very popular option" with "plenty of evidence" of public support. "I think there's a case for that. The case is essentially a democratic case," he said.

His move towards staging a two-question poll comes after several weeks of mounting pressure from David Cameron and Nick Clegg to clarify his plans for the referendum, which is due to take place in 2014 or 2015.

Although he confirmed that he expects 16- and 17-year-olds will be allowed to vote in the referendum, for the first time in British electoral history, Salmond has so far refused to publish details about the proposal, including the exact questions.

During last week's Tory party conference, Cameron taunted the first minister for his reticence, accusing him of being a "big feartie", running scared of the voters, because he knew independence did not have majority support. At the Liberal Democrat conference, Clegg challenged Salmond to have "the courage of his convictions" by holding a single-question "yes or no" referendum.

But, said Salmond, the Tories and the Lib Dems had "no mandate whatsoever, not a scintilla of a mandate" in Scotland, having come a poor third and fourth at elections in 2010 and 2011, and could not jointly command a majority in Scotland.

"It's absurd for a prime minister to assume he has any legitimacy in instructing the Scottish parliament when it should hold a referendum on Scotland's constitutional future, when we've got an impeccable mandate reinforced by a massive popular assent while they've no mandate whatsoever. The days of Tory PMs telling Scotland what to do are over," he said.

The vote on Scottish independence is now almost certain to take place, after Salmond won an unprecedented victory in May's elections for the devolved Scottish parliament, winning the first overall majority at Holyrood.

Many observers expect the referendum to be staged before or around the next UK general election in May 2015, but polling shows the SNP has yet to convince a majority of voters to support full independence, making a less dramatic second option very attractive to Salmond.

Recent polls suggest up to 38% of Scots support independence, but the vast majority of polls and the most authoritative studies of Scottish public opinion show that fiscal autonomy within the UK – an option known as "devo max" – is the most popular option by two to one.

Under that option, the Scottish parliament would raise all its own taxes and run its own welfare system, but would share services such as defence, overseas aid and foreign affairs with the rest of the UK. Holyrood currently controls all education, health, policing, local taxation, environment and domestic transport policies.

The UK government is pushing for further measures to give Holyrood control over income tax rates, allow it to borrow at least £2.2bn and set other minor taxes through Westminster as part of the Scotland bill, as ministers speed up devolution across the UK. The Welsh and Northern Irish governments are also likely to get further minor tax and financial powers: Stormont was given control last month of air passenger duty.

Offering Scots a second referendum option might make life difficult for Clegg and the Lib Dems in the UK government. On Saturday, the Scottish Lib Dems agreed to reinvigorate their campaign for Scottish "home rule" within the UK. This position is close to fiscal autonomy, but Willie Rennie, the leader of the Scottish Lib Dems, insisted their proposal was to introduce fiscal federalism for all parts of the UK, not to give Scotland special treatment.

However Danny Alexander, the chief secretary to the Treasury and the most senior Scot in the UK cabinet, ruled out any significant extra powers for Scotland in the near future, beyond new measures in the Scotland bill, suggesting he would object to any Lib Dem support for Salmond's second question. He said those would "take years to work out", and that should be prioritised. "I don't rule out further change, but I would say that the most important thing is to take [on] the provisions in the Scotland bill, which are hugely ambitious, hugely significant actually and in some ways more significant than devolution itself. This is the biggest shift in financial powers and accountability within the UK for 300 years."

Salmond said that Donald Dewar, the architect of Scottish devolution, had set a precedent when Labour's devolution referendum in 1997 asked voters to make a choice about devolution and whether or not to give Holyrood tax-altering powers. The answer was "yes" to both.

Salmond said civic society groups, pressure groups such as Reform Scotland and senior businessmen such as Jim McColl, an advocate of greater fiscal powers for Scotland had indicated "broad support" for a second option. They could back a non-party campaign for fiscal autonomy. "So people then vote for independence or the status quo [or] they could also vote for fiscal autonomy or the status quo. Not, incidentally, three questions on a ballot paper: two questions á la 1997," he said.

Cameron has accepted that Salmond has a clear mandate to stage the referendum without interference from UK government, but senior figures in the coalition and Labour are exploring options for Westminster to influence or oversee the vote.

They have raised fears that the Scottish government could skew the referendum by setting a biased question, using unfair methods of choosing voters or fixing unfair rules for campaign donations. Labour sources have said the Electoral Commission should be allowed to set the questions and rules for donations.