The Prime Minister has been asked to reappraise his position on Scotland's financial and constitutional future following a landslide victory for the SNP.
Scottish Finance Secretary John Swinney said his leader Alex Salmond, who has been returned as First Minister with the first parliamentary majority in Holyrood history, told the Prime Minister that the SNP's resounding victory was a game changer.
Mr Swinney told BBC Radio Scotland's Good Morning Scotland programme: "The First Minister made clear yesterday his intention to discuss with the Prime Minister the importance of recognising the difference that yesterday's result produces for Scotland.
"The difference is the people of Scotland have made it very clear that they want to see progress made on the questions of economic opportunity in Scotland, and on constitutional progress.
"The short term opportunity to do that is by improving and strengthening the Scotland Bill, currently going through the UK parliament, and that is the message that the First Minister gave to the Prime Minister."
The Scotland Bill is designed to give Scotland greater financial accountability, but the SNP has argued it does not give the Scottish Government sufficient levers to grow Scotland's economy.
The Bill passed its final stage in Holyrood in the last term and is currently being debated at Westminster, but Mr Cameron has been told the outcome of the Scottish election should have a bearing on the outcome of these deliberations.
Mr Swinney said: "I think the Prime Minister and the UK government have got to, if they have the slightest bit of seriousness about the respect agenda, to respect not the Scottish Government, but respect the Scottish people.
"And the people of Scotland have delivered an astonishingly clear and comprehensive outcome to the election campaign by returning the SNP to government with an absolute majority."
Mr Swinney, who led the SNP between 2000 and 2004, rejected suggestions that Westminster could interfere with an independence referendum in Scotland.
He said: "We can legislate for there to be a referendum on independence within Scotland, and we will do that in the latter part of the parliament.
"But the early priority is to get the necessary economic and financial powers that will enable us to work our way out of the economic challenges that we face.
"We've done a lot in the last four years to deal with an exceptional period of economic turbulence."
He added: "The reason we need more economic powers is to better respond to that, and to deliver the type of opportunities the people of Scotland asked of us when they gave us such a handsome mandate in the election yesterday."
Mr Swinney said the SNP's new parliamentary majority will give him the opportunity to revisit previously unsuccessful policies such as minimum pricing for alcohol.
He said: "The other parties have got to learn some lessons from this election campaign.
"Lets take an issue like minimum pricing, for example. I was very struck when I went round the doors by the anger and incredulity of members of the public, saying they couldn't believe other parties had stood in our way in tackling Scotland's unhealthy relationship with alcohol."
He said the Scottish Government would try to build consensus rather than wield its majority to force through legislation or score points for political gain.
However, he said Labour Party "no longer has a significant role in Scottish politics".
He added: "I think they've lost their purpose. I think they've got a lot of thinking to do about what they're about and what they want to do."
A meeting of the SNP's national executive committee is due to take place later today at Edinburgh's Macdonald Holyrood Hotel, in the shadow of the Scottish Parliament, alongside the first group meeting of the party's 69 newly elected MSPs.
The first meeting of the new parliamentary session will take place on Wednesday when members are sworn in.
The new Presiding Officer and two deputies will also be elected.
Scottish Conservative deputy leader Murdo Fraser called on Mr Salmond to "bring it on" and launch an immediate independence referendum, otherwise there would be a "very persuasive argument" for Westminster to steal his thunder.
He said: "Nothing would be more damaging for Scotland than to have four or five years of a long running debate over whether we will be independent or not."
He added: "Bring it on. If we're going to have a referendum we should have it as soon as possible so we can get the question settled once and for all."
Mr Fraser said the UK government should give "very serious consideration" to launching its own referendum on the UK's constitutional future.
He said: "If Alex Salmond is feart to bring forward his referendum to the Scottish people now, perhaps that is something that should be done for him."
Scottish Labour deputy leader Johann Lamont recognised the challenge her party faces in choosing a new leader following the planned resignation of Iain Gray after the party was reduced to 37 MSPs.
She added: "It's a simple fact that if you lose as many seats that we've lost then you're choosing from a smaller pool of people."
She added: "We will have leader in the autumn. Very often the world defines big hitters in whatever way but under pressure, with the challenges ahead, leadership will always emerge.
"But critically, although we will be diminished team, the first place to go will be to build the team itself and rebuild our confidence inside the parliament."
Ms Lamont tentatively suggested that she could be up for the job.
She said: "I'm a potential leader because I'm deputy leader, but I've barely slept since Thursday so I'm not going make that decision now."
Liberal Democrat chief whip Alistair Carmichael, MP for Orkney and Shetland, borrowed a phrase from US President Barack Obama and said his party had been given "an absolute shellacking" at the Holyrood election.
He said: "We've got a small group in the parliament who are going to have to do a lot of heavy lifting, but if I had to sit down with a list and say that I could only have five MSPs I think it would look pretty much like the five we've got.
"We may not have the quantity, but we have tremendous quality in that group in Holyrood."