In a direct address to people in England, Wales and Northern Ireland, the Scottish first minister added: "Although you can't vote SNP your views do matter to me and you have a right to know what to expect of my party if the votes of the Scottish people give us influence in a hung parliament.
"If the SNP emerges from this election in a position of influence we will exercise that influence responsibly and constructively, and we will always seek to exercise it in the interests of people not just in Scotland but across the whole of the UK."
Increase spending by 0.5% a year, providing an extra £140bn to support the economy and public services, including an extra £24bn for the NHS across the UK
Set an annual UK target to build 100,000 affordable homes
Increase the minimum wage to £8.70 by 2020
Restore the 50p top income tax rate for those earning over £150,000
Support an increase in the Employment Allowance from £2,000 per business per year to £6,000, to help smaller firms take on more staff
Oppose the "£3bn cut" in disability support
Keep the triple lock on pensions and protect the winter fuel allowance.
By Brian Taylor, BBC Scotland political editor
It would have been easy, so easy, for the SNP manifesto launch to slide towards bombast. The elements were all there.
The polls suggest a substantial lead for the Nationalists. The venue was, literally, cavernous and crowded with eager supporters - who were ready to cheer volubly at any mention of independence, Scotland or indeed Nicola Sturgeon.
Sheffield, anyone? Not a chance. After eight years in devolved government, Ms Sturgeon is nothing if not cautious. Her mood was cool, serious and controlled, with elements of self-effacing humour.
Something truly extraordinary happened this morning.
A woman who is not even a candidate in this election; whose party is running in just one of the four nations and which, even if it does as spectacularly well as some polls suggest, would have just one in 13 MPs in Westminster pledged to build not just a "stronger Scotland" but a "better and more progressive politics for everyone" in the UK.
Nicola Sturgeon showed once again why she is the undoubted star of this general election campaign and why she says her Inbox is filled with emails from voters from outside Scotland who want the chance to vote SNP.
Labour last week put at the heart of its manifesto that, if elected, it would get the government's deficit and debt down in the course of the next parliament, and to that end there would be cuts in non-protected public services (or everything but schools, health and overseas aid).
It did that partly because all its polling showed that in England it would need to demonstrate what it thinks of as "fiscal credibility" to get a hearing from undecided voters.
So it is quite definitely not an act of amity and solidarity with its putative Labour brothers for the SNP, led by Nicola Sturgeon, to tell voters that she'll get the Tories out, get Labour in and make sure Labour won't stick to its fiscal promises.
The Scottish National Party "will always support independence" says its leader Nicola Sturgeon - but after the proposition was rejected in last year's referendum, she has set her sights on a staging post.
The immediate constitutional goal is now for Scotland to gain control of all taxation, including North Sea revenues, loosening the ties that bind the United Kingdom together.
The SNP manifesto launched today ditches the dismal name for this policy of "full fiscal autonomy" in favour of "full fiscal responsibility" and "full financial responsibility."
Scottish Liberal Democrat Alistair Carmichael said the SNP manifesto had confirmed a £180bn borrowing plan which would cost £3.1bn a year in interest repayments alone.
And the Scottish secretary said Ms Sturgeon's backing for full fiscal autonomy - which would see Scotland gain control of all its own tax powers - would create a £40bn black hole Scotland's finances.
"This is a manifesto of short-term thinking leading to long-term debt," he explained.
"Instead of taking the opportunity to map a route out of debt, Nicola Sturgeon is sticking with a plan to plunge the country further into it.
Conservative leader David Cameron said of the SNP manifesto: "You would see our deficit climbing up again, you'd see spending on Welfare soaring again, businesses crushed again, jobs lost again.
"With Labour and the SNP, our economy will head into ruin again. And who will pay? You will pay with higher taxes."
Scottish Labour leader Jim Murphy said the SNP had previously described last year's independence referendum as a "once-in-a-generation event" and had broken a promise to the people by refusing to rule out another one.
Mr Murphy added: "When you look at all the pressures in Scotland - the growing gap between the poor and the prosperous, the crisis in the NHS and the number of people stuck on zero hours contracts, then Scotland surely has higher priorities than thinking about another referendum.
"This is a 'say one thing do another' manifesto. They claim to support a UK-wide mansion tax at the same time as committing to cutting Scotland off from UK-wide taxes."
Meanwhile, UKIP leader Nigel Farage said Mr Cameron, Mr Miliband and Lib Dem leader Nick Clegg had shown "appalling weakness" and accused them of engaging in "outright appeasement" in the face of aggressive SNP tactics.
He said: "All three of them have guaranteed the continuation of the Barnett Formula in its present guise, ripping-off English voters and throwing truckloads of English money over Hadrian's Wall.
"And none of them will guarantee that only English MPs will vote on English laws in the next parliament, meaning that any new influx of SNP MPs will be able to dictate the governance of England.