Ms Sturgeon, who is Scotland’s first minister, has backed calls for another referendum on Brexit – a so-called People’s Vote.
She has also said she wants another referendum on Scottish independence within the next two years if the UK leaves the EU.
Among the manifesto’s key pledges are:
Working with other parties across the UK to “stop Brexit”
Backing another EU referendum with Remain as an option
Offering a choice for Scotland to become an independent, European nation
Supporting Article 50 being revoked if the only alternative is a no-deal Brexit
Speaking at the manifesto launch in Glasgow, Ms Sturgeon urged voters to back the SNP in order to “send the powerful message that Scotland is for Europe”.
She added: “We can stand up for Scotland’s right to be heard, and we can proclaim our determination to remain a European nation.
“On 23 May people can send Theresa May – or whoever comes after her – a strong and resolute message: Stop Brexit and let’s keep Scotland at the very heart of Europe.”
Ms Sturgeon said her party was willing to work with others across the UK to give people a “final say” on whether the UK should leave the EU, and insisted that there is now “a real chance to keep Scotland in the European Union.”
She said: “Any Brexit deal agreed by Westminster must be put to the people with Remain on the ballot paper. If no deal is the only alternative, Article 50 must be revoked.
“Scotland must have the choice of becoming an independent, European nation – and we can proclaim our determination to remain a European nation.”
Ms Sturgeon went on to accuse the UK Government of having “ignored the overwhelming vote in Scotland” from the 2016 EU referendum, when 62% of Scottish voters backed the UK remaining in the EU.
She claimed the Conservative government at Westminster had “dismissed all attempts at compromise from the Scottish government” and had also “disregarded, time and again, the views of the Scottish Parliament”.
The SNP leader added: “Taking Scotland out of the EU against our will does not deliver on the result of the referendum.
“For people in Scotland, pressing ahead with Brexit doesn’t deliver on the referendum, it overturns that referendum.
“And Brexit does something else: it gives the lie to the notion that Labour and the Tories see the United Kingdom as a partnership of equal nations.”
With Theresa May having outlined plans to leave Downing Street, Ms Sturgeon said the prospect of Boris Johnson becoming the next prime minister was now “a deadly serious possibility and for Scotland it would be a nightmare”.
The first minister said: “Faced with Brexit – and very possibly an extreme Farage-Johnson style Brexit – people in Scotland deserve the right to decide whether Scotland should become an independent member of the EU instead.”
And she said the SNP’s “positive, progressive” manifesto for the vote “makes clear our determination to stay in the EU”.
Ms Sturgeon added: “In this manifesto you will see strong and unequivocal support for free movement. It is good for Scotland and it is good for Europe.
“The SNP celebrates and values all those who choose to make Scotland their home, and SNP MEPs will take that welcoming message to the heart of Europe.”
The SNP won two of Scotland’s six seats in the European Parliament at the last EU election in 2014.