Nicola Sturgeon has refused to rule out withholding the Scottish National party’s support from a Labour budget if Jeremy Corbyn as prime minister failed to give Holyrood the powers necessary to hold an independence referendum in 2020.

In a further toughening of her stance, Sturgeon said she would offer SNP support to a Labour minority government only if it accepted the principle that it is for Holyrood to decide the timing of the second referendum.

Asked if she could be definitive that her party would vote down a Labour budget if Corbyn refused the section 30 order needed by Holyrood to organise a vote next year, Sturgeon told the Guardian: “The principle is that the fact of and the timing of an independence referendum should be for the Scottish parliament, elected by the Scottish people, to decide.

“I just don’t believe, if you have the potential for a minority Labour government, they are going to turn their back on the ability to govern over the question of a year.”

Pressed on whether voters should believe that the SNP would scupper a minority Labour administration similarly over the issue of one year, the first minister replied: “The SNP under my leadership would not ever, in any circumstances, vote for a Conservative Queen’s speech or budget.

“We will be offering support to a minority Labour government. We’re simply saying that principle should be respected.”

Sturgeon and Corbyn clashed bitterly on this question earlier in the campaign, with Corbyn rejecting Sturgeon’s offer of a “progressive alliance” to defeat Boris Johnson and accusing her of being willing to usher in “another heartless Conservative government”.

But in recent weeks Labour has revealed itself to be increasingly open to the prospect of a second independence referendum in 2021 if Scotland returns a pro-independence majority in that year’s Holyrood elections.

Next year is already a busy one for Scotland, with the potential for another EU referendum and preparations for the Holyrood election campaign. The former SNP leader Alex Salmond’s trial for a series of alleged sexual assaults is set for March, and Glasgow will host a UN climate conference in November. Would an independence campaign get the focus it merits?

Dismissing the Salmond trial as “irrelevant in this context”, Sturgeon replied: “If you take the future of the UK in the European Union, the whole climate change issue, these are all relevant in terms of Scotland’s ability to shape its own future.

“I think it’s important if we are to allow ourselves to have the maximum potential to shape our own future, as opposed to have it shaped for us, that we have the ability to do so on that timescale.”

In contrast to Corbyn, Boris Johnson has pledged to deny the Scottish government a section 30 order under any circumstances. Holyrood’s constitutional relations secretary, Michael Russell, hinted earlier in the election campaign that the Scottish government could resort to legal action in that case.

Sturgeon refused to elaborate, saying: “We’ll consider all the options but I’m not going to get into the detail of that right now. People have got the right over the next few days of having the focus being on do we want Boris Johnson to be in the position of calling these shots or don’t we?”

Nicola Sturgeon steps off her battlebus in Lanark, where she visited the Wallace tea rooms. Photograph: Jane Barlow/PA

Speaking to the Guardian from the SNP’s yellow election battlebus, Sturgeon said: “Personally I’ve found this to be quite a happy and warm campaign, even though it’s been bloody freezing outside.”

One of the SNP’s central messages has been about “locking the Tories out of Downing Street”. However, polling suggests the main SNP gains will be from Labour, which is predicted to lose all but one of its six Scottish seats.

Asked whether this represented a failure of strategy, Sturgeon said: “Polls don’t decide elections and nothing is inevitable. For as long as there is time left to make the argument, I’ll make the argument that Scotland should play its part in locking the Tories out of government. And the SNP is the best place to try and do that.”

Despite gloomy predictions during the summer about the impact on the Scottish Tories’ fortunes of the departure of their leader Ruth Davidson and Johnson becoming head of the UK party, their support does not appear to have dipped significantly.

The latest polling for the Sunday Times Scotland put the SNP on 39%, down one point since last month, and the Conservatives up one on 29%. Why are so many Scots still voting Tory? Challenging the polls again, Sturgeon said: “I don’t know that they are. I’ll have that conversation next week and I’ll keep campaigning to stop that happening.”

There is the possibility that those who support the union – support for remaining within the UK was up two points to 53%, according to the Sunday Times Scotland poll – are lending the Tories their votes. The Scottish Tories have run a highly personalised campaign focused on Sturgeon’s independence demands, in the hope this could sway undecideds. Meanwhile, Sturgeon in the final week of campaigning is emphasising that a vote for the SNP on Thursday need not be a vote for independence.

“I’ve spoken to countless people on this campaign trail who have said to me they are not SNP voters normally, and they wouldn’t necessarily vote for independence in a referendum, but they want to make sure they vote in a way that maximises the chances of keeping the Tories out of government.

“There’s no doubt that there’s a narrative, discussion and consideration around tactical voting in this election that I have not experienced previously.”

With the SNP running second in all Scottish Tory seats, she added: “People understand that this election is not going to decide the issue of independence. People may well vote SNP to keep the Tories out, given the crossroads and the prospect of Boris Johnson for five years.”