She said: “While we don’t know the final tally of seats right now, it looks as if it is beyond any doubt that there will be a pro-independence majority in that Scottish Parliament.
"And by any normal standard of democracy that majority should have the commitments it made to the people of Scotland honoured.
“So for any Westminster politician who tries to stand in the way of that I would say two things. Firstly, you are not picking a fight with the SNP, you are picking a fight with the democratic wishes of the Scottish people and secondly you will not succeed.
“The only people who can decide the future of Scotland are the Scottish people and no Westminster politician can or should stand in the way of that.
Ms Sturgeon said the timing of an independence referendum should be for the Scottish Parliament to make.
She said: “That is not a decision for Boris Johnson or for any Westminster politician.”
UK environment secretary George Eustice had earlier said granting a second independence referendum in Scotland would be “irresponsible”.
Ms Sturgeon has vowed to plough ahead with plans for a follow-up border poll as her party’s chances of taking more than 65 seats in the Scottish Parliament remained in the balance as counting closed in on a finish on Saturday.
With the SNP leader’s strategy putting her on a collision course with the Prime Minister, who has insisted he would not support an “irresponsible” referendum, Mr Eustice said it was the wrong time to be considering another plebiscite.
“We think this is a complete distraction,” Mr Eustice told Times Radio.
“It would be irresponsible to have another divisive referendum and another bout of constitutional debate at a time when we are charting our way out of this pandemic and when we’ve got to really focus on economic recovery.
“We think it’s completely the wrong thing to be doing.
“We had a referendum just a little over five years ago and that settled the issue.”
Ms Sturgeon’s party gained three seats during the count on Friday – the only party to take a constituency from another – winning Ayr, Edinburgh Central and East Lothian.
However, uncertainty continued into Saturday, as the wins picked up by the SNP could cause the party to lose regional seats under Holyrood’s system, cancelling out gains made.
Labour deputy leader Jackie Baillie held on to her Dumbarton constituency, which had been the most marginal seat in all of Scotland and a top target for the SNP.
Ms Baillie had a majority of just 109 in the 2016 Scottish Parliament election, but increased that to 1,483.
With some constituencies still to be counted on Saturday, when the crucial regional list results will also be declared, Ms Sturgeon said victory is “not impossible”.
Mr Eustice’s comments come after Boris Johnson told the Daily Telegraph another referendum would be “irresponsible and reckless” in the “current context” as Britain emerges from the coronavirus crisis.
The environment secretary looked to shift the conversation away from there being a clash in the courts between No 10 and the SNP over the issue.
Asked whether the UK Government would fight any bid for a second Scottish referendum in the courts, he told BBC Breakfast: “Look, I’m not a lawyer – lawyers will look at these things and I think it is getting ahead of ourselves.
“There is a question at the moment over whether the SNP will get a majority or not – we’ll have to wait and see until the results come through.”
Scotland’s deputy first minister John Swinney said he was “very confident” Holyrood would emerge from the Super Thursday elections with a pro-independence majority, even if the SNP falls short of winning more than 65 seats.
The SNP picked up key seats in Edinburgh Central, Ayr and East Lothian on Friday, and have continued their surge on Saturday afternoon.
But under Holyrood’s proportional representation system, those successes could see it lose out on the regional list which make up the remaining 56 seats.
Mr Swinney told the BBC: “I think what matters on the question you asked me about, a mandate for a referendum is what is the position of those who are elected to the Parliament and will there be an overall majority of members elected committed to the hosting of an independence referendum, and I’m very confident that will be the case.”
Scottish Conservatives leader Douglas Ross admitted the prospect of the SNP winning an outright majority was "absolutely on a knife-edge".
"They were only two seats short going in, they have a net gain of one at the moment, so clearly it is extremely close," he told BBC Scotland.
"It will come down to the last few seats and last few votes and we have got to wait until we see the final picture."
In England, the post-mortem into Labour’s poor showing at the polls has continued as a senior party figure said it was evident after the Hartlepool by-election defeat and local election losses that voters “do not now see Labour as answering” their concerns.
Shadow home secretary Nick Thomas-Symonds said there would be a policy review to “make sure… our party is connected in communities up and down the country”.
He said it would be up to leader Sir Keir Starmer – who called the results “bitterly disappointing” – on whether to embark on a reshuffle of his top team but there was a “wider, more fundamental issue” at play for the party than personnel changes.