Nicola Sturgeon will put ending austerity, the removal of nuclear weapons from Scotland and a second independence referendum in 2020 at the heart of her party’s post-election negotiations with Labour if there is a hung parliament.

The Scottish National party (SNP) leader said those worried about a Jeremy Corbyn government should be reassured that her party would insist on zero tolerance of antisemitism, Islamophobia and any form of racism.

Setting out the list of demands as she launched her party’s general election manifesto in Glasgow on Wednesday, she told activists that the SNP would “put Scotland’s interests front and centre in a progressive alliance to lock the Tories out of government at Westminster”.

Calling for a “real end to austerity”, she stressed that the next UK government must make right the cumulative cuts Scotland has been hit by over the past decade, which she estimated to be £13.9bn.

Reminding activists of the financial package agreed by Theresa May with the Democratic Unionist party (DUP) after the 2017 election, Sturgeon told activists: “A party seeking our support must be prepared to set out how they would repair the damage of a decade of austerity and put back the money that has been lost.”

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Sturgeon said she would negotiate to increase NHS spending in England and Wales by £136 a head, bringing it to Scottish levels and involving an extra spend of £35bn by 2023-24, although no information was made available about how that figure was calculated. She is also proposing an NHS Protection Act that would include a double lock for devolved assemblies to consent to any post-Brexit trade deal.

Attacking Labour’s proposed windfall tax on the North Sea oil and gas industry as the latest example of Westminster “pocketing” Scotland’s oil revenue, she contrasted this with £200bn to renew the “immoral” Trident, saying: “A key SNP demand for our support will be the removal of Trident from Scotland and saving of billions of pounds to be invested instead in our precious public services.”

Emphasising that Brexit “is nowhere near being done”, in a reversal of Boris Johnson’s catchphrase, she said: “Scotland will pay a heavy price for the Tories’ Brexit obsession and Labour’s neutrality.”

Describing an SNP victory in Scottish seats as “a clear instruction” that voters want a second independence referendum in 2020, she said: “People are becoming increasingly sick of hearing Boris Johnson and Jeremy Corbyn talking about not allowing Scottish people to choose their own future.” To cheers and applause, she added: “Well I’ve got news for them: it’s not up to you.

“My message to any party seeking SNP support after the election is: if you cannot support this most fundamental of democratic principles then the SNP cannot and will not support you.”

Taking questions from the media after her speech, Sturgeon was challenged on whether she would continue to support Corbyn in a minority government given the renewed heavy criticism of his handling of antisemitism.

Paul Edlin, the president of the Glasgow Jewish Representative Council, told the Scottish Daily Mail on Wednesday that Sturgeon would be doing “a deal with the devil” if she were to help Corbyn into Downing Street.

She responded: “I deplore Jeremy Corbyn’s lack of leadership on antisemitism,” adding that the SNP would exercise its influence “responsibly” in any post-election negotiations. “We would not be signing any blank cheque to Jeremy Corbyn or to any leader,” she said.

“In addition to all of the other things, we would be very clear in our expectations to any party leader who wanted the support of the SNP to make clear its zero tolerance of antisemitism, Islamophobia, to any form of prejudice or racism. And to those worried about Jeremy Corbyn, it should give a degree of reassurance that SNP MPs are able to apply that pressure.”

Asked whether she believed Corbyn was personally antisemitic, she replied: “I don’t know Jeremy Corbyn personally well enough to answer that question, but I do say unequivocally and emphatically that he has failed to get to grips with this problem within his party.”

She said Boris Johnson had “a charge sheet of his own to answer” on racism.

Sturgeon refused to say whether she would support moves to replace Corbyn as Labour leader in order to facilitate a post-election deal. “I don’t choose the leader of the Labour party, I wouldn’t choose Jeremy Corbyn, but I’m not in charge of that decision.”