It was the first time the SNP had suggested it would use its domination at the polls to press ahead with its plan to split Scotland from the rest of Britain.
Until now, the party leadership has always promised that it would not use the general election results to re-open the debate about independence.
Asked if Scotland was now closer to independence after the landslide, Salmond said: "Yes, because the SNP now has an overwhelming mandate from the Scottish people to carry forward Scotland's interests. The base of the confidence of people in Scotland is growing all the time. Now, obviously the timing of any future referendum is a matter for the Scottish people first and foremost."
SNP leader Nicola Sturgeon attempted to play down the idea that her party was already campaigning for a new referendum, insisting this was not her immediate goal.
Newly returned British Prime Minister David Cameron used his Cabinet reshuffle to promote one of his most determined pro-union ministers to oversee sweeping plans to devolve unprecedented powers to the government of Scotland.
Chris Grayling, the former Justice Secretary, becomes Leader of the Commons, in which he will also lead ground-breaking reforms to the way Parliament works intended to ban Scottish MPs from being able to have the final say over English laws.
Grayling said he would allow Scotland to have the "strongest" devolved government of any country on earth. This would give Scotland the power to raise certain taxes and set benefit payments, but the Scottish Government would also be held responsible by voters for its decisions over putting up tax.
Privately, senior Tories are happy for the SNP - who want to end austerity - to be given more powers because they will pay the price for raising taxes in the electoral system.
Cameron promoted Michael Gove, the former chief whip, to the post of Justice Secretary.
However, senior party figures warned up to 60 MPs were preparing to demand that Cameron adopt far tougher plans to scale back the powers of the European Union, before a referendum is held by 2017.
Anti-austerity campaigners descended on Downing Street and Whitehall yesterday to protest against the new Conservative Government. Four people were arrested for public order offences and a fifth for assaulting a police officer.
Elsewhere, political parties continued to digest the shock general election results, which saw Nick Clegg, Nigel Farage and Ed Miliband all resign as party leaders.
Several Labour MPs prepared to enter the contest to succeed Miliband, while senior figures urged members to "skip a generation" and choose a fresh face, untainted by the past.
One of the favourites to succeed Miliband, the shadow business secretary Chuka Umunna, has set out his stall as a modernising, centre-ground, pro-business candidate. Umunna is one of half a dozen prominent Labour figures believed to be considering throwing their hats in to the ring to succeed Miliband. Others include Yvette Cooper, Andy Burnham, Tristram Hunt, Liz Kendall and Dan Jarvis.
Pollsters probe errors
Pollsters who wrongly predicted the election result have launched an investigation into what went awry.
Polling giant YouGov has said its probe into the embarrassing blunder would not jump to any "hasty conclusions" and would "take the time" to examine the causes.
Polling companies across the board had believed Labour and Conservatives were neck-and-neck. But the Tories secured 331 seats, just over the 325 they needed to control half of the House of Commons. Tory MPs now make up 50.9 per cent of the 650 seats in Parliament, but the Tories won only 36.9 per cent of all votes cast. Labour has 232 MPs, 35.7 per cent of the total after securing 30.4 per cent of the vote.
No polling company correctly predicted the seven point lead that the Conservatives achieved.
YouGov president Peter Kellner said: "What seems to have gone wrong is that people said one thing, and they did something else at the ballot box."
Sir Robert Worcester, the founder of polling firm Mori, also suggested very late changes in voters' intentions were behind the error. He blamed this on two factors. Firstly, the "English tendency to hold on to nurse" - in other words to decide, in the cold light of a polling station, to change their mind and back an incumbent Prime Minister rather than gamble on an untested alternative.
Secondly, the rise of the SNP, which may have intimidated wavering voters into voting Tory after all. "In 1992, Neil Kinnock blew it in the final week with hubris," said Worcester. "People who had said they intended to vote Labour shifted to the Liberal Democrats very late, and the polls missed that. You had [SNP leader] Nicola Sturgeon flaunting the power she was going to have under a Labour government, and my sense is that in England that persuaded some Ukip voters to move over to the Tories."
- additional reporting PA, Observer, Daily Mail
