Talks with other devolved leaders were held at Downing Street.
Sturgeon: Our Voice Will Be Heard
SNP leader Nicola Sturgeon has insisted Scotland will no longer be ''sidelined or ignored'' at Westminster.
The First Minister said the landslide victory - which saw the SNP claim all but three of the constituencies north of the border - had given the nationalists a ''mandate on a scale unprecedented for any political party, not just in Scotland but right across the UK''.
Half of those who voted in Scotland backed the SNP on Thursday, with the party winning 1,454,436 votes across the country.
While that has resulted in a record number of nationalist MPs at Westminster, it remains unclear how much influence they will be able to exert after David Cameron's Conservatives won a shock majority government.
But as she gathered with her group of MPs, Ms Sturgeon said they would now be pressing for an end to austerity.
She insisted: ''Our message to Westminster is simple, our message to the politicians of the other parties at Westminster is this one - no longer will Scotland be sidelined or ignored in Westminster.
''Our voice will be heard. Our interests will be protected.''
The First Minister, whose party had had just six MPs after the 2010 election, stated: ''Scotland has given the SNP a mandate on a scale unprecedented for any political party, not just in Scotland but right across the UK.
''We will use that mandate to speak up for and protect the interests of Scotland.
''Let us be very clear, the people of Scotland on Thursday voted for an SNP manifesto which had ending austerity as its number one priority, and that is the priority that these men and women will now take to the very heart of the Westminster agenda.''
Ms Sturgeon said: ''After Thursday, and as I told the Prime Minister when I spoke to him yesterday, it simply cannot be and it will not be business as usual when it comes to Westminster's dealing with Scotland.''
Ms Sturgeon said she was ''absolutely delighted'' and ''bursting with pride'' at her party's massively expanded group of MPs.
''The people of Scotland have spoken and the people have placed their trust in the SNP to represent Scotland at Westminster as well as at Holyrood,'' she said.
''Just as voters in almost every part of this nation of ours chose the SNP our pledge is that these 56 SNP MPs will represent the interest of all of Scotland.
''We will represent in Westminster, just as we do in the Scottish Parliament, people in every corner of our country, people who voted Yes in the referendum as well as people who voted No. People who voted for us on Thursday and people who did not.
''Our job is to repay the trust you have shown in us and I pledge today that that is exactly what we will do.''
She said in the general election Scotland had spoken ''more loudly and more clearly than ever before'' and added: ``My message today to Westminster is this - Scotland's voice will be heard in Westminster now more loudly that it has ever been before.''
She continued: ''As we promised in the campaign that strong voice will be a voice for more progressive politics.
''We will continue to seek to reach out to people of progressive opinion right across the UK, so we can put an end to austerity, invest in our public services like our precious National Health Service, invest in a stronger economy to get more young people into jobs. We will work with others to put those priorities right at the heart of Westminster.
''That is what people in Scotland have tasked the SNP now with doing.''
After the event Ms Sturgeon was questioned on how SNP MPs would exert influence with a Conservative majority government.
She said: ''We've got a majority Tory government with a fairly slender majority, that's the first point.
''Secondly we've got 56 MPs that are not there to settle down and just become part of the establishment as we've seen all too often with Labour MPs elected from Scotland. These are MPs who are going with a mandate to speak up for Scotland.
''Thirdly this is a point I made to the Prime Minister directly yesterday, his Government cannot ignore what happened in Scotland on Thursday. People spoke with a very loud voice and that voice said we want change, we want an end to austerity we want a more empowered Scottish Parliament and the Westminster government cannot ignore that, it cannot be business as usual.''
Commenting on speculation David Cameron could be prepared to offer Scotland full fiscal autonomy she said: ''That's not what David Cameron indicated to me yesterday but that was a brief discussion that we'll follow up in the weeks to come.
''I want to see a more empowered Scottish Parliament, I don't think the Smith Commission proposals go far enough.
''We set out in our manifesto the priority powers we think require to be devolved to Scotland, powers over employment, the minimum wage, business taxes, welfare.
''These are the levers we need to get our hands on if we're to grow our economy faster and get more people into jobs and tackle poverty more effectively.
''So these will be the priorities that SNP MPs are arguing for.''
Scottish Liberal Democrat leader Willie Rennie claimed the SNP were now ''redefining their mandate'' with calls for more powers to be devolved to Holyrood.
He argued: ''They said a vote for the SNP was a vote for more public spending and against Trident. Apparently we weren't really listening and they really meant they would demand more powers.
''The radical new powers agreed by the all-party Smith Commission, including the SNP, matched the spirit of the referendum. The SNP are now trying to undermine that work.
''They are demanding powers for Holyrood that will create an unstable form of devolution that exists nowhere else in the world. Despite the rhetoric from the SNP during the election they are still fixated with the constitution and taking Scotland to independence.''
Stefano Brizzi is accused of murdering the Scottish police officer.
It happened in the Govanhill area at lunchtime.
It's being treated as attempted murder.
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