Nicola Sturgeon said the SNP would "shake up the Westminster establishment" and make the rest of the UK take notice of Scotland in the upcoming general election.
The SNP leader said the ballot in May represented an "historic moment" where people could "shift the balance of power from the corridors of Westminster to the streets and communities of Scotland".
Polls are suggesting that the Scottish nationalists could win dozens of seats in the election, and could hold the balance of power.
Ms Sturgeon pledged today that if there is a hung parliament, SNP MPs would "vote to stop a Tory Government even getting off the ground".
She then called on Labour's Ed Miliband to do the same and commit to working with the Nationalists to "lock David Cameron out of Downing street".
With less than six weeks to go till the general election, the big UK parties are "weaker than ever before", she said.
In contrast support for the SNP continues to rise, with Ms Sturgeon announcing membership of her party now stands at 102,143.
She told the SNP conference in Glasgow: "T he only way for Scotland to shake up the Westminster establishment is to vote SNP."
Ms Sturgeon said if her party is in a position of influence at Westminster SNP MPs would " demand an alternative to slash and burn austerity".
Keeping the NHS in public hands would be another priority, she said, along with voting against any replacement for the Trident nuclear weapons system, which is based in Scotland on the Clyde.
The Scottish First Minister said: " At a time when in-work poverty is on the rise and people are being forced to use food banks, when public services are under strain and conventional defence forces are being cut to the bone, we will stand firm and unwavering against a single brass penny - let alone £100 billion - being spent on the obscene status symbol that is a new generation of Trident nuclear weapons."
In the run up to the general election she said there would " continue to be talk of the deals that might be done after the election".
Ms Sturgeon vowed: "W e will work every day to protect Scotland's interests and to make your voice heard.
"We will seek to use whatever influence you give us to call a halt to ever deeper austerity, to protect our NHS and to say loudly and clearly that the precious resources of our country should be invested in the future of our children, not in nuclear bombs.
"We will use our influence to win for our Scottish Parliament the full financial and social powers that it needs to grow our economy and create more jobs.
"And we will work in a spirit of friendship and co-operation with others who share our ideals - we will work with everyone, wherever they may be in the UK, who wants to see greater fairness and prosperity at the heart of their communities too."
Ms Sturgeon, who was given a six minute long standing ovation from the audience in the conference hall, used her speech to reach out to people south of the border,
She spoke to the "ordinary people across these islands who feel just as let down by that out-of-touch Westminster system as we do" and told them she had " a message of friendship and solidarity".
She said: "I won't pretend that the SNP doesn't still want Scotland to be independent.
"I think I can safely say that we do still want Scotland to be independent!
"But at this general election - with the power of the big parties weaker than ever before - I say this to people of progressive opinion all across the UK.
"As long as Scotland remains part of the Westminster system, we will be your allies in seeking to shake up and reform that outdated and discredited system once and for all."
She continued: "T o people in England, Wales and Northern Ireland, I make this promise.
"The SNP stands ready to work with you in making that positive change for all of us."
She recalled that in minority government at Holyrood the SNP had restored free education, abolished prescription charges and frozen the council tax.
"We can - and we will - use that experience in a minority led House of Commons to get good things done there too," she said.
While Labour politicians have argued that voting SNP will simply increase David Cameron's chances of getting back into government, Ms Sturgeon insisted: " Let me said it loud and let me make it clear - the SNP will never put the Tories into government.
"Not now. Not ever."
She said that " as long as there are more anti-Tory MPs - Labour or SNP - than there are Tory MPs in the House of Commons, we can keep them out of government".
She added that was a "matter of simple arithmetic" and said: " If there are more anti-Tory than Tory MPs after the election, the only way the Tories get back into power is if Labour lets them back in.
"So in the interests of total clarity, let me make this promise today.
"If there is a hung Parliament, SNP MPs will vote to stop a Tory Government even getting off the ground.
"I call on Labour, today, to match that pledge - to make clear that if Labour and the SNP combined have more seats than the Tories, they will join forces with us in a vote of confidence to lock David Cameron out of Downing Street."
Ms Sturgeon said a vote for the SNP was " a vote to make sure that the Tories are replaced with a better alternative."
She told the conference: " If you want a Labour government to have backbone and guts, you need to elect SNP MPs to provide it for them.
" And if you want a Labour government that won't just be a carbon copy of the Tories, but will instead deliver the real change Scotland needs, then you must elect SNP MPs to force Labour's hand and keep them honest."
Despite the SNP's lead in opinion polls in Scotland, Ms Sturgeon said her party still had "a mountain to climb" in the election.
"We have six MPs," she stated.
" In most of the other 53 seats in Scotland, we face hefty majorities.
"The biggest number of MPs we have ever had at Westminster is 11."
Despite that though, she said: " No constituency is off limits for the SNP in this election. We will fight for every vote and every seat."
SNP MPs at Westminster would back a £2 rise in the minimum wage, taking it to £8.70 by 2020, the end of the next UK parliamentary term.
She also set out her goal of making Scotland a "Living Wage nation", with a target of having 500 companies paying this to their workers in the next 12 months.
To help youngsters stay on at school and college, she announced the Educational Maintenance Allowance would be extended.
While 35,000 teenagers currently receive the payments of up to £30 a week, she said more school pupils and part time college students would be eligible for the grant.
"From next year a total of 57,000 16 to 19 year olds will be entitled to receive and Educational Maintenance Allowance," she stated.
To great cheers from the audience she insisted it was "time to abolish the House of Lords".
Ms Sturgeon said it had "no place in a democratic society" and added: "People with no democratic mandate should not be writing the laws of the land."
She also announced a new fund of £20 million would be set up in Scotland in a bid to tackle violence against women.
The First Minister said: "We will invest that money to speed up the court process, give more support to victims and expand schemes to help offenders change their behaviour."
Scottish Labour leader Jim Murphy said: "No-one will be fooled by Nicola Sturgeon's claims to be the UK's best friend when the SNP's entire purpose is trying to break up Britain.
"There was no mention today of the austerity max that would be inflicted on Scotland if the SNP were to follow through on their policy of full fiscal autonomy.
"The First Minister knows, but won't admit, that SNP sums don't add up and her economic plans would lead to a £7.6 billion black hole in tax revenues."
He added: "Despite all the cheering and backslapping the facts remain only Labour or the Tories can form the next UK government. Any seat taken from Labour by the SNP or anyone else simply helps David Cameron to stay in power.
"Unlike the SNP, Labour has a real plan to tackle austerity and deliver real social justice, a plan that will see those that have most paying more in taxes to help those that have least.
"The SNP do not support our tax policies so there is a clear choice at the election. If you want change and you want a change of government then Labour is that change. The only way to get a Labour government is to vote Labour."
Scottish Liberal Democrat party president Malcolm Bruce MP said: " Nicola Sturgeon's £180 billion borrowing plans threaten to wreck the economic recovery across the UK.
"We know that the cost of interest repayments alone would be equivalent to a new secondary school every other day. They haven't learnt the lessons of the last economic crash.
"It is not liberal or progressive to leave an ever growing mountain of debt for future generations to pay.
"The Conservatives want to cut too much, putting at risk public services, and the SNP want to borrow even more than Labour, threatening our economic recovery.
"We will not spend today what our children should have tomorrow. Only the Liberal Democrats have a clear and affordable plan to create a stronger economy and fairer society for Scotland where we will balance the books by 2018 and invest an extra £800 million in the Scottish NHS."