Prime Minister David Cameron has spoken to Nicola Sturgeon and "reiterated his commitment to governing with respect and implementing devolution".
It comes as Scotland's First Minister issued a warning to Mr Cameron that "Scotland's voice has to be heard'' after the SNP comprehensively routed Labour north of the border, winning an historic 56 Westminster seats.
While Mr Cameron pledged to give Holyrood ''important powers over taxation'', the Conservative leader does not appear to be offering any substantial new devolution.
The official Twitter channel for the Prime Minister's office confirmed the two leaders have now spoken after the watershed General Election left the UK divided, with the Tories winning an unexpected majority across the UK, but north of the border the SNP saw its tally of MPs surge from six five years ago.
Ms Sturgeon said she "made it clear" to Mr Cameron that "it cannot be business as usual" during the brief conversation today.
Tories face criticism over election campaign
Speaking on STV News, the SNP leader said: "Scotland didn't just vote in small numbers for a different party. Some of the swings we saw across Scotland were unprecedented in Westminster political history. Scotland decisively voted against austerity and for an alternative approach.
"I briefly spoke to the Prime Minister this afternoon and made it clear that it cannot be business as usual, the democratic will of the Scottish people as expressed in that election yesterday has to be recognised."
Labour, which had taken 41 seats north of the border in 2010, was left with just one Scottish MP, with Scottish party leader Jim Murphy and election campaign chief Douglas Alexander among those who lost their seats.
While Ed Miliband announced he is stepping down as UK leader of the party, Mr Murphy insisted he will stay in his job in Scotland in a bid to rebuild his ailing party.
In an unprecedented night for the SNP, it took all seven of the seats in Glasgow, Scotland's largest city, with shadow Scottish secretary Margaret Curran among the losers there.
Former leader Alex Salmond was returned to Westminster as the new MP for Gordon after seizing the constituency from the Liberal Democrats.
Leaders set to meet soon
Talking about her conversation with the Prime Minister, Ms Sturgeon said: "It was a brief call. It was an opportunity for me to congratulate him, I didn't want him to be Prime Minister again but he has won the election and I congratulated him. He was gracious to congratulate the SNP on our success. We will meet as soon as possible and discuss these issues in more detail but I made it clear, it can't be business as usual.
"I wanted an anti-Tory majority and the polls suggested there would be an anti-Tory majority - I made clear if that had been the outcome I would have wanted to work with Ed Miliband to have him in Downing Street rather than David Cameron. Ed Miliband had seemed unsure if he would have wanted to do that, but that now is academic. I think that is regrettable but it's not to do with what happened in Scotland - even if Labour had held all of their Scottish seats yesterday they still wouldn't have done enough in England to beat the Tories.
"I said during the election that this election wasn't about independence and it wasn't a vote for a second referendum. I said very explicitly and directly to voters across Scotland that if you vote for the SNP I will not take your vote as an endorsement of independence. I am not going to turn my back on that, I'm going to stick to my word. If there is ever another referendum in Scotland on independence that will only come about if people vote for that in a Scottish Parliament election. Yesterday's election was a vote to make Scotland's voice heard at Westminster."
Senior figures from the Lib Dems were also ousted in the nationalist landslide, with Danny Alexander, who had been chief secretary to the Treasury, and former party leader Charles Kennedy both ejected from the Commons.
Ms Sturgeon's party won 50% of the votes cast in Scotland, compared to just 20% in 2010. In comparison Labour saw its share of the vote fall to 24%, with the Conservatives on just under 15% in Scotland and the Lib Dems on 7.5%.
Labour's Ian Murray managed to retain his Edinburgh South seat in the face of the SNP tsunami, as did Liberal Democrat Alistair Carmichael, who held on to Orkney and Shetland with a reduced share of the vote.
David Mundell, who was Scotland's only Conservative MP in 2010, is still the single Tory representative north of the border.
As the results came in Mr Salmond declared that the ''Scottish lion has roared''.
Ms Sturgeon said: ''The political firmament, the tectonic plates in Scottish politics have shifted. What we are seeing is a historic watershed.''
After returning to Downing Street, Mr Cameron said he would ''stay true to my word'' and implement plans for further devolution that have already been drawn up ''as fast as I can''.
He stated: ''Governing with respect means recognising that the different nations of our United Kingdom have their own governments as well as the United Kingdom government.