Alex Neil says he does not expect a second referendum before the next Scottish Parliament elections in 2021, but he argues there is support across the parties for another boost to devolution.
And he says the cross-party Scottish Constitutional Convention, which drew up the blueprint for the parliament, should be reconvened to agree an expansion of powers, including taking control of future referendums.
Mr Neil said: “There is broad agreement in parliament, even among some Tories – leaving aside the argument about post-Brexit powers – on the need to go much further.
“It’s ridiculous, for instance, that we have only got control over the rates and bands of incomes tax and no control over the tax on savings and dividends.
“We could now devolve that inside the UK because it was EU rules which stopped it last time.
“I would try to get broad-based agreement and consensus between people who are pro-independence and people who are anti-independence but believe in much more devolution of power from Westminster.”
He said a key aspiration from such a process should be securing for Holyrood the power to call a referendum on any issue “without requiring specific permission from Westminster”.
He said: “That would mean any future decision on the timing of a referendum on independence, or anything else, would be entirely in the hands of the Scottish Parliament and not the Westminster parliament.”
The details of the 2014 independence vote were decided in the Edinburgh Agreement signed by former First Minister Alex Salmond and the then Prime Minister David Cameron ahead of the referendum.
But when Ms Sturgeon announced her ambition for a second referendum last year, Theresa May insisted “Now is not the time” and refused to discuss arrangements.
Pro-independence campaigners fear any future move to hold a referendum will run into similar problems.
Ms Sturgeon has said she will decide later this year whether to push for a second independence vote, but Mr Neil does not expect her to go for another referendum yet.
“We’ve got to see how Brexit turns out. We might not know until near the end of the transition period the detail of the trade agreement with the EU, and that could affect how we define independence post-Brexit.”
But he said reconvening the constitutional convention would allow progress to continue. “Saying no to a referendum before 2021 does not mean we need to freeze Scotland’s constitutional arrangements,” he said.
The convention, launched in 1989, brought together Labour, Lib Dems, Greens, trade unions, churches, business people and others to hammer out a devolution blueprint. The SNP withdrew at an early stage and the Tories did not take part.