The SNP leader insists her manifesto pledge to "undertake new work, starting this summer, with the aim of persuading a clear majority of people in Scotland that independence is the best future for our country" was backed by almost half of voters in the Scottish election on Thursday.
The Conservatives, who scored a record 20% of the vote to become Scotland's second biggest party, have pledged to oppose another referendum and make life difficult for the SNP on policies that they oppose.
But Sturgeon told BBC One's Sunday Politics Scotland she is "not going to be thwarted in my determination to govern in the interests of the country as a whole".
When asked if Scotland can put an independence referendum to bed for the next five years, Ms Sturgeon said: "No, the position I put forward in the SNP manifesto got the support of almost 50% of the population."
She said the Tories "were the only ones going in with an unequivocal position of saying No to another independence referendum and they got just over 20% of the vote".
"It's a ridiculous notion to say that because the Conservatives managed to get scarcely over 20% of the vote that somehow the case for independence has taken a step back - the contrary is the case," she said.
"There is an independence-supporting majority in the Scottish Parliament if you take the SNPs and the Greens.
"My manifesto said in certain circumstances the Scottish Parliament should have the right to propose another referendum."
She added: "I have got to persuade other people of the strength of my case, and in saying that, I am prepared to do that patiently, with a lot of humility and listening to people."
Speaking on the same programme, Scottish Conservative deputy leader Jackson Carlaw said the SNP would be "incredibly foolish" to stage another referendum, and that he "wouldn't be unhappy" if the UK Government blocked it.
"It wasn't in their manifesto, I don't think they have the mandate, and I think Scotland has now made it very clear that it wants to see the government get on with governing the country, and to put the independence issue aside for this parliament," he said.
"I think if the SNP has got any sense it will recognise that if it pushes on now and persists with trying to put Scotland through another referendum, it is actually going to come to grief."
Asked if the UK Government should try to prevent a second vote on independence, he added: "I wouldn't be unhappy if they did, but I actually don't believe it is going to get to that point."
But Sturgeon said the Tories would set themselves "on a collision course with the Scottish population" if they stand in the way of a "clear demand" for another referendum, she said.
"If we get into a situation where the Tories decide to be a roadblock to the democratic will of the Scottish people I think the Tories will find themselves, with any talk of a recovery which I think they are perhaps overstating right now, with that recovery coming to a juddering halt," she said.
Carlaw also confirmed the Tories' intention to frustrate the SNP on its "named person" scheme and any attempt to make taxes higher than the rest of the UK.
He said there is a "natural majority" against named person and the Tories "want to stop it".
"I believe there is a considerable natural majority across other parties, that have come to realise the concerns there are with it with the public," he said.
"I believe that is where we will make a difference. It is one of the first policies we will."
The SNP will also need to build cross-party alliances to get its budget through.
Carlaw said: "Our concern is to ensure that taxes overall are no higher here in Scotland than they are in the United Kingdom."
Sturgeon said: "I will seek support for the totality of the Budget, and I will put forward a Budget that I think is in the best interests of Scotland.
"I'll reach out and seek areas of common ground, but I'm not going to be thwarted in my determination to govern in the interests of the country as a whole."
She added: "I think named person is the right thing. I think Jackson Carlaw is wrong, although we will see, I don't think he will find that there is a majority in the Scottish Parliament in the way he says there is but we will see how that develops."
She said she has "work to do" to address the "unfounded concerns" of some parents about the named person scheme.
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