Scotland's First Minister has pledged the SNP will put ending austerity at the "heart of the Westminster agenda" at the same time as she called on David Cameron to transfer more powers to Holyrood as a "matter of priority".

Nicola Sturgeon said that after last week's "truly historic" general election, which saw her party win an unprecedented 56 out of 59 Scottish seats, she would press the Prime Minister for further devolution.

While a package of new powers for the Scottish Parliament has already been agreed, the SNP leader said that in the wake of the election result David Cameron must agree to extend these "even further".

She said the election result, in which the SNP secured 50% of the votes cast in Scotland, gave her party a "unique obligation" to "reach out and speak for all of Scotland".

Ms Sturgeon told MSPs at Holyrood: "I pledge today that we will make Scotland's voice heard."

She vowed the SNP group at Westminster would "stand up for the progressive politics that we put at the heart of the campaign".

She added that while Scotland had voted for change, it was a matter of "regret" the Conservatives had won an overall majority at Westminster.

The First Minister pledged Scottish nationalists in the Commons would be a "constructive, principled, determined and effective opposition to the majority Tory government", adding they would do this on behalf of people "not just in Scotland but people right across the UK".

Ms Sturgeon vowed: "We will build alliances to argue for the protection of the vulnerable against deeper welfare cuts, we will seek to defend our human rights protections, to halt further privatisation of the NHS and to safeguard the UK's place in Europe.

"A clear majority of people across the UK did not vote Tory last Thursday and they deserve a strong voice in Parliament.

"I promise today that the SNP and the Scottish Government will seek to be that voice."

The First Minister went on to state that the scale of the SNP victory last week would strengthen the Scottish Government's hand in its efforts to "secure the very best deal for Scotland at Westminster".

With Ms Sturgeon expected to meet the Prime Minister later this week, she said that both public spending and protecting Scotland's budget would be "key issues on the agenda".

But she added that the issue of more powers for Holyrood would also be raised.

The Scottish Government has consistently argued that the package put forward in the wake of the Smith Commission does not go far enough, with Ms Sturgeon saying: "The outcome of the election makes abundantly clear that this view is shared by a significant proportion of the Scottish electorate."

She added: "If the Prime Minister and his Government mean what they say about respecting the outcome of the election in Scotland, they must now agree with us a process that looks again at the Smith Commission proposals, with a view to extending devolution even further. That must be a process that is made in Scotland - and one that involves wider Scottish society.

"As my party's manifesto made clear, we believe that the Scottish Parliament should move to full financial responsibility.

"However, as a matter of priority, we want to see devolution of powers over employment policy, including the minimum wage, welfare, business taxes, national insurance and equality policy - the powers we need to create jobs, grow revenues and lift people out of poverty.

"It is such a package of priority, job-creating, poverty-tackling powers that we will now seek to build support for and agreement on."

Ms Sturgeon urged Labour, which lost all but one of the the 41 Scottish seats it had held at Westminster, to work with them on this.

"For Labour to argue that these powers should remain in the hands of a majority Tory government with no mandate in Scotland would be inexplicable to most people across Scotland," the First Minister said.

"I genuinely hope Labour will now think again and join us in arguing for a powerhouse Scottish Parliament, equipped with the powers we need to build economic prosperity and foster greater social justice."

She also said the Conservative Party had a "clear choice" about what it should do now.

The Tories recorded their lowest ever share of the vote in Scotland since 1865 in last Thursday's election, Ms Sturgeon said, adding that Mr Cameron and his party could either "ignore the voice of the Scottish people and carry on regardless" or could alternatively "choose to demonstrate that Westminster does listen and that it is capable of serving Scotland better".

Throughout the election campaign the SNP leader insisted that a victory for her party would not result in another independence referendum.

She said today: "Let me be absolutely clear that I stand by that.

"There will only be another independence referendum if the people of Scotland vote in a future Scottish Parliament election to have one. That is democracy.

"And, of course, it cuts both ways. I can't impose a referendum against the will of the Scottish people, but nor can David Cameron rule out a referendum against the will of the people. It will be the people who decide."

Scottish Labour deputy leader Kezia Dugdale wished the SNP's "strong team at Westminster" well, and urged them to oppose Conservative efforts to repeal the Human Rights Act.

"These benches will do everything that we can to oppose any attempt that the Tories make to scrap the Human Rights Act," she said.

"Enacted in the early days of a fresh Labour government full of hope and aspiration for the future, the Act embodies the civil and political rights which are fundamental to any liberal democracy."

Ms Dugdale also said there is "fear and trepidation in the air" in Scottish communities over Tory plans to "attack disability benefits".

Ms Sturgeon said: "Opposition to the repeal of the Human Rights Act is one example of, I hope, many examples where Labour and the SNP in that progressive alliance that I have talked about can work together against the wrong-headed measures being put forward by the Conservative Government."

She added: "Rather than us simply standing here in this Parliament trying to mitigate measures from a Westminster Conservative Government, I say this in all sincerity to Kezia Dugdale: let us join together in saying 'Put the welfare powers in the hands of this Parliament and this Government so we can stop these attacks in the first place'."

Scottish Conservative leader Ruth Davidson congratulated Ms Sturgeon on the SNP's election performance, and also Prime Minister David Cameron "in managing what no Prime Minister has done since 1955 - increasing the number of votes and seats while already in office".

She said: "While in Scotland we did not manage to add to the seats total, we did contribute to the share of the vote with 434,000 fellow Scots voting for the Conservative Party - the most in any election since devolution."

Ms Sturgeon said: "I really do hope in the days following this statement we have a different tone struck from Ruth Davidson.

"The Tories scored the lowest percentage share of the vote in Scotland since 1865 - that is a fact - and the SNP scored a record high."

While the number of votes cast for the Conservatives increased from 2010, the much larger overall turnout in the election meant their share of the vote went down.

Scottish Liberal Democrat leader Willie Rennie said his party has "lessons to learn" from the election which saw his party reduced to a rump in Westminster.

But he attacked Ms Sturgeon for using Scottish Parliament time to make a statement on an election result in the UK Parliament.

"This week, police with guns on the streets of Stirling, mental health services falling short, unemployment on the rise, accident and emergency times missed for months on end," he said.

"Yet this First Minister spends parliamentary time with this self-congratulatory SNP party statement which tells us absolutely nothing new.

"Can I ask the First Minister when she is going to give a statement on even just one of these important issues?"

Ms Sturgeon said: "Well, I am standing in this very place tomorrow to answer First Minister's Questions, as I do every Thursday.

"I'm not sure if Willie Rennie has got a question tomorrow as the strength of his party is such that he doesn't get one every week, but that is hardly my fault."

The Liberal Democrats have just five MSPs in the Scottish Parliament, which means they are not entitled to a weekly question at FMQs.

Ms Sturgeon added: "The decisions that the Westminster Government take impact directly on the ability of this Government and this Parliament to serve the people of Scotland, so I make no apology."

Scottish Green co-convener Patrick Harvie welcomed the First Minister's discussions with the Scottish Trade Union Congress (STUC) on "the very direct threat to the right to strike coming from the new UK Government".

"If the STUC's proposals for workplace devolution come back on to the agenda, will she ensure that such proposals have no place in Scotland?" he asked.

Ms Sturgeon said: "This Government will stand against any attempt by the Conservative majority Government to crack down on trade union rights."

SNP MSP Chic Brodie sought confirmation that the SNP will seek a "double majority" in any vote to leave the EU, to ensure that a vote to leave requires a majority Yes vote in each of the constituent countries of the UK.

Ms Sturgeon said: "If there is an EU referendum Bill placed before the House of Commons, our MPs will lay amendments to that Bill to introduce a double majority rule.

"For the UK to come out of the EU, it is not enough for the UK as whole simply to vote for that.

"Each and every member of what we were told was 'a family of nations' must also do that."

SNP MSP Stewart Stevenson urged Ms Sturgeon to oppose the "democratic affront" of defeated Labour MPs seeking a route back to Westminster through appointment to the House of Lords.

He said: "In particular, given that the Liberals have 101 members - more even than the the total numbers in the US Senate - but now that they are down to eight MPs, is it time for around 80 or 90 of the existing ones to consider resignation."

Ms Sturgeon called for the "democratic outrage" of the House of Lords to be abolished.

"People with no democratic mandate should not be writing the laws of our land," she said.