Nicola Sturgeon has used her first speech as SNP leader to predict the party could hold the "balance of power" after the next general election.
Ms Sturgeon said the SNP would never do a deal which would put the Conservatives into power in the event of a hung parliament.
She said Scotland could win concessions from a Labour government at Westminster that depended on SNP MPs for support.
But a deal would depend on commitments including scrapping Trident.
The SNP is aiming to win a majority of Scottish Westminster seats next May, with recent polls suggesting the party is on track to significantly increase the six seats it already holds.
Speaking at the SNP's annual conference in Perth, Ms Sturgeon said the odds on a hung parliament - in which no single party has an overall majority at Westminster - were shortening every day.
But she described claims that voting Labour would keep out the Conservatives as the "biggest con trick in Scottish politics", and said Scotland had still "ended up with the Tories" despite voting Labour at the last general election.
Ms Sturgeon added: "Scotland could well hold the balance of power in a Westminster parliament with no overall majority.
"If that happens, I promise our country this. You won't need to have voted Labour to keep the Tories out, because that's what we'll do.
"My pledge to Scotland today is simple - the SNP will never, ever, put the Tories into government.
"But I ask you to think about this. Think about how much more we could win for Scotland from a Westminster Labour government if they had to depend on SNP votes."
Ms Sturgeon said Labour would be forced to "deliver real powers for our parliament" as well as rethinking the "endless austerity that impoverishes our children" and thinking again about "putting a new generation of Trident nuclear weapons on the River Clyde."
And she said Labour's alliance with the Tories in the "No" campaign ahead of the independence referendum proved the party had "lost its soul".
Ms Sturgeon, who will become Scottish first minister next week, had earlier said succeeding Alex Salmond as SNP leader was the "proudest moment of my life".
She paid tribute to Mr Salmond as a "champion of our nation" and a "hero of our movement".
And she said the SNP's best days were still to come, despite the "No" vote in September's referendum.
Ms Sturgeon also used her speech to pledge that the Scottish government would double the hours of childcare available to three and four years olds from 16 hours a week to thirty hours a week if it wins the next Holyrood election in 2016.
She said she wanted to "unite this country in a national endeavour to give every child - no matter their background - the best opportunity in life."
"We already deliver 16 hours a week of free childcare for all three and four-years-old. From August next year, that entitlement will extend to 27% of two-year-olds as well," she added.
"That is more hours of childcare than in any other part of the UK and we should be proud of that. But so important is good quality, extensive childcare to the school performance and life chances of young people, that we will go further still.
"I pledge today that our 2016 manifesto will set out an ambitious plan to increase childcare provision.
"By the end of the next parliament, my commitment is that all 3 and 4 year olds and all eligible 2 years olds will receive, not 16 hours, but 30 hours of free childcare each week."
And she also said the small business bonus - which will help almost 100,000 small businesses next year to the tune of £165m - will continue for the entire lifetime of the next parliament if the party is re-elected.
And she vowed that the revenue budget of the Scottish NHS would rise in real terms for the remainder of this parliament and for "each and every year of the next parliament too" if she is re-elected as first minister in 2016.
The new SNP leader will reveal her first programme for government to the Scottish Parliament in less than two weeks time, saying this would set out the "legislation and policies that will shape our priorities until the next election".
She told the conference: "At its heart will be radical action on land reform, empowering communities, raising attainment in our schools and tackling some of the deep injustices in our society, like domestic abuse and gender inequality."
She identified low pay as an issue that "needs to be addressed" as she announced all Scottish government contracts from now on would make payment of the living wage a priority.
The Scottish government already pays its staff and all those working in the NHS the living wage, but Ms Sturgeon said some sub-contracted cleaners working in its offices earned less that this.
"We wanted to put that right, so I am pleased be able to confirm today that the Scottish government has struck a deal with its cleaning contractor, Mitie. That deal will see all 117 staff who are currently paid below the living wage brought up to that level by the end of this year," she said.
"And in future, although we cannot mandate it in law, each and every new Scottish Government contract will have payment of the living wage as a central priority."