However, it is understood the Prime Minister made clear the “absolute focus” of the UK should be on dealing with the cost-of-living crisis and other challenges instead.
Ms Sturgeon wants to hold a referendum on October 19 next year, but whether or not it takes place rests on a ruling by the Supreme Court, which has been asked to decide if this is within Holyrood’s powers.
After the meeting, a Scottish Government spokesman said the discussion was “constructive and cordial”, with both leaders agreeing to work together on the cost-of-living crisis.
He said Ms Sturgeon had emphasised the need for benefits to rise in line with inflation and had told Mr Sunak to provide more funding for pay rises for NHS and other workers.
And the spokesman added: “The First Minister made clear she intends to honour the manifesto commitment and the electoral mandate for an independence referendum and that the Scottish Government remains ready and willing to negotiate a process to enable that to happen.”
The first face-to-face encounter between the two leaders marked something of a milestone on the road to what could be more functional relationship between the UK and Scottish governments.
What were once frosty relations headed into the deep freeze under Mr Sunak’s predecessor Liz Truss, who notoriously described Ms Sturgeon as an “attention seeker” who was best ignored during her campaign for the Tory leadership.
She later turned out to be as good as her word, breaking with convention by refusing to call the First Minister or her Welsh counterpart Mark Drakeford when she became Prime Minister. She left office having never spoken to either of them.
By contrast, Mr Sunak called both leaders the day he took office. On Thursday he became the first Prime Minister to open the British-Irish Council summit since Gordon Brown in 2007.
Ahead of the meeting, the First Minister’s spokesman said any thawing of the relations between the two governments would be progress.
“Hopefully we’ll get to a place where we have a constructive relationship, even if we don't agree on everything,” he said.
“Liz Truss wasn't in office very long, as we know, but given some of the pronouncements she made during her premiership, even having a meeting is important.
“The FM hopes to continue a dialogue in a constructive relationship with the new PM.
"We’re clearly not going to agree on a range of things, but that shouldn’t stop us having a grown up sensible, constructive relationship.”
Behind the scenes, UK Government officials are also hoping that working together with the Scottish Government on areas of mutual interest – at the same time as politely, but firmly refusing Ms Sturgeon’s requests for indyref2 – is what most Scottish voters want.
Former Scottish secretary David Mundell told the BBC there was unlikely to be a “substantive change” in policy towards the devolved nations under Mr Sunak, but that unlike Ms Truss he would “reach out” and “do business where that can be done”.
Polling expert Sir John Curtice said it was easy for Mr Sunak to talk about mutual respect between the nations, but the real test would be how willing he was to compromise on policies.
“I think it will be interesting to see what is his definition is of the UK and devolved governments ‘working together’,” he said.
“Johnson and Truss’s definition of the governments working together was basically ‘the UK Government sets the parameters and we expect you guys to help us implement it’, or ‘we are willing to spend money in devolved areas and we don't care about the fact that we tread on your toes’.
“It’ll be interesting to see whether or not the UK Government is willing to be more inclusive.
"Rather than saying ‘this is the policy and what are you going to do about it?’, is it going to be more willing to say, ‘let's work together to decide what we think a sensible policy should be for dealing with X, Y, or Z’?”
The meeting took place as Mr Hunt called the coming autumn statement one of the “biggest responsibilities” of his political career, amid intense speculation about what his budget will contain.
Writing in his local paper, the Chancellor offered little clue of what measures he was planning, but warned his constituents of the need to “put our national finances back on an even keel”.
Tax rises and tough spending cuts are expected in the budget, which will come as Mr Sunak and his Chancellor attempt to restore confidence in the UK economy after Ms Truss’s administration.
The South West Surrey MP apologised to readers of the Farnham Herald for the break in his weekly column, but assured them he had been “heads down, including over Saturday and Sunday, preparing the autumn statement with the Prime Minister”.
“It is an extremely difficult challenge because after Covid, many people have got used to the state being able to step in with limitless resources to fix big problems,” he said.
“But in the end, as every family and business knows, you have to find a way to pay for things,” he wrote.
Mr Sunak and Mr Hunt are considering imposing up to £60 billion in tax rises and spending cuts in the autumn budget on November 17, in what will prove a major test for the new Tory administration.
Downing Street is facing fresh calls not to axe the scheduled social care cap as a way of avoiding deeper cuts elsewhere.
The Prime Minister was reviewing whether to delay the plans by two years to 2025, Whitehall officials confirmed on Thursday, amid fears it could be put off indefinitely.
The potential move has alarmed charities, with The Alzheimer’s Society warning ministers they “must not roll back on the care cap”, which it described as a “crucial first step to tackle catastrophic care costs”.
Mr Hunt was tight-lipped in his column about any of the rumours and reports about his budget measures, but told readers: “These are tough times for people everywhere.
“But we are a resilient, tough and resourceful country and have seen off even greater challenges many times before.”
He also addressed the Bank of England’s decision to hike interest rates from 2.25% to 3%, in its biggest single rise for 33 years.
“It is, of course, very challenging that base rates have just increased again but it is vitally important the Bank of England continues to do its job to restore the stability that comes with low inflation,” Mr Hunt said.
The Chancellor, twice defeated in Tory leadership contests, was elevated to one of the most powerful jobs in the country in the dying days of Ms Truss’s premiership before being kept on by Mr Sunak.
Signing off his column, he turned his attention to the “brilliant” local businesses in his locality.
“Delivering the Autumn Statement will be perhaps one of the biggest responsibilities I have undertaken in public life and I will be thinking hard how to help every single one of them,” he said.