In a BBC interview, Mr Jack, pictured right, suggested a generation could be “25 or 40 years”.
First Minister Nicola Sturgeon accused him of a “rage against democracy” that would not prevail in blocking indyref2.
Meanwhile, former Tory minister Lord Dunlop has said Boris Johnson urgently needs a clear strategy to counter rising support for independence.
Ten opinion polls since June have suggested a majority now favour Scottish independence, with 54% on average backing yes.
The UK government has consistently opposed a new vote, and Mr Jack has sought to harden this position.
When asked if ministers were ruling out a referendum for the full term of the next Scottish Parliament, regardless of the election outcome, he said “it’s no for a generation”.
Asked to define a generation, he said: “Is it 25 years or is it 40 years – you tell me? But it’s certainly not six years nor 10”.
The SNP argue that this pre-election position will change if they win at Holyrood in 2021 with a clear manifesto commitment to hold another independence referendum.
Speaking after hosting a virtual meeting of the British-Irish Council, Ms Sturgeon said that “the people of Scotland will decide the future of Scotland”.
She added: “I think we are seeing played out in another part of the world today that politicians don’t get to stand against democracy,
“Power comes from people not from politicians and the will of the people in any country has to prevail and so I don’t treat those comments with too much in the way of seriousness”.
The apparent increase in support for independence is fuelling debate about strategy on both sides of Scotland’s constitutional divide, with six months to go until the next Scottish Parliament election.
Lord Dunlop has called on Boris Johnson to demonstrate “strong leadership and statesmanship” and urgently come up with a “clear, coherent and consistent strategy for the Union”.
The former Scotland office minister wants more co-operation between the UK and devolved governments with a new forum in which they would take decisions together.
Having reviewed the workings of the Union for the prime minister, he said he was “very disappointed” the report he submitted a year ago had not yet been published or fully implemented.
He was also critical of the UK government’s internal market bill as an expression of a more “muscular unionism” that he believes risks “alienating moderate and middle-of-the-road Scots”.
Mr Jack insisted the bill was necessary to protect jobs and trade throughout the UK and that there was a strategy to bolster the Union.
Analysis – anxiety on both sides?
The next Holyrood election, due in exactly six months, will certainly be about how best to overcome the coronavirus crisis.
It will also be about who’s best placed to take the key decisions and whether that should be tested in another independence referendum.
Nicola Sturgeon has already made clear she will include an explicit commitment to indyref2 in the SNP manifesto.
But some on the “yes” side are anxious for a plan B because Boris Johnson refused a referendum request after the 2019 election and Alister Jack is now seeking to rule one out “for a generation”.
There’s anxiety in the “no” camp too because support for independence appears to have risen above 50% on Mr Johnson’s watch.
The referendum in 2014 may have answered the independence question but it did not settle the debate, which is now finding new energy in post-Brexit politics and a global pandemic.
It’s a dirty job but someone’s got to do it – Prime Minister Boris Johnson has appointed himself minister for the Union.
Boris Johnson has appointed himself minister for the Union and set up a special Cabinet committee, typically chaired by Michael Gove.
There is also a small Union-focused team in Number 10 led by former MP Luke Graham and a larger Union directorate emerging in the Cabinet Office.
Mr Jack argued that UK investment in road and rail infrastructure, city deals and Covid recovery in Scotland would help to win people over.
He was speaking to the BBC in the UK government’s new Scottish headquarters in Edinburgh, which is to become home to 3,000 civil servants from 10 different departments.
“It’s a big statement from the UK government that we are absolutely embedded in Scotland,” he said.The UK government’s opposition to another referendum has prompted some in the SNP to demand their party considers alternative routes to independence.
Inverclyde councillor Chris McEleny wants a “Plan B” that would treat an election victory for independence-supporting parties at Holyrood as a mandate for leaving the UK, if a referendum cannot be agreed.
“A democratic election is a legitimate way for people in Scotland to express that they wish Scotland to be an independent country,” he said.
Former MP Roger Mullin, who has been an SNP member for 55 years, said it may also be possible for Holyrood to have an advisory referendum without Westminster’s consent.
“We cannot allow Boris Johnson to have a veto,” he said.
The SNP leadership has indicated that a Catalonia-style referendum, without UK government agreement, would damage their cause. But some in the party believe the legality of such a route should be tested in court first.
Yessers make their point in a march through Glasgow.
For many in the SNP and the wider yes movement, this debate is driven by impatience for independence.
For some it’s also a way of expressing wider concerns over policy and the huge rift between Nicola Sturgeon and her predecessor, Alex Salmond, exposed by the Holyrood inquiry into how harassment complaints against him were handled.
The SNP’s longest serving MP Pete Wishart has warned against infighting, arguing that “the Tories are counting on impatience, frustration and fragmentation doing their job for them”.
“They know they can’t beat us, so they’re hoping that somehow we manage to beat ourselves,” he said. “We should not oblige them.”
He thinks alternatives to an agreed referendum should only be considered if and when that option is exhausted.
Better Together two?
If there was another independence referendum it’s not clear who would lead the no campaign.
Mr Jack said it had not been discussed because “we’re not having” a referendum.
Scottish Labour’s deputy leader Jackie Baillie, pictured right, said she was “not convinced” there could be another cross-party Better Together campaign.
She said Boris Johnson had become “the SNP’s best recruiting sergeant” and that Labour would want to campaign for further devolution in Scotland and the English regions.