Mr Salmond said his party now occupied the political high ground
Scotland's first minister has challenged Gordon Brown to "change his policy or change his job" after the SNP's Glasgow East by-election victory.
Alex Salmond said the poll had been a test of strength between his Scottish Government and UK Prime Minister Mr Brown's Labour government in London.
The SNP overturned a Labour majority of 13,507 to win the seat by 365 votes.
Mr Salmond said the result proved the SNP now controlled the political agenda in Scotland.
The first minister, who was greeted with loud cheers and applause from SNP party members as he arrived for a triumphant press conference at the Glasgow Fort shopping centre in the east end of the city, paid tribute to the campaign run by victorious candidate John Mason.
He said: "The theme that John developed during the campaign was to send a message to Gordon Brown and to send it in clear and unmistakeable terms - that message is change your policy or change your job.
"This by-election was unique - this was a by-election which was a test of strength between the Labour London government led by Gordon Brown and an SNP government in Scotland doing its best for the Scottish people.
"That was a test of strength that the Labour party set the timing of. It was in their third safest seat in the whole of Scotland. That was the test of strength, and it was London Labour that was found wanting and the SNP in Scotland that emerged victorious. We now command the agenda in Scottish politics."
Mr Salmond said the test for his party was now how it used its political influence to benefit the people of Glasgow East, and of Scotland as a whole.
He added: "What we need for the people of the country is a change of policy. We need action - action against rising prices which are hitting family budgets, action against energy costs, action to inject more demand into the economy."
'Political high ground'
The first minister said the Glasgow East result proved there were now no safe seats anywhere in Scotland for Labour, adding: "I understand that on the swing that John achieved yesterday Tom Clarke would be the sole remaining Labour MP in Scotland.
"They used to say it was the Tories who could only get one MP in Scotland."
Mr Salmond claimed the SNP now occupied the political high ground because it was "putting the people's priorities first."
"We will march to the sound and the priorities of the people of Scotland," he pledged.
"If we keep doing that then we are going to take some stopping come the general election and the Scottish election to come, and the independence referendum in 2010."
The SNP win took most political commentators by surprise, with Mr Salmond's confident prediction of victory during the campaign described in some quarters as a "major political gamble."
And the first minister, well-known for his love of a flutter on horse racing, confessed to the assembled media: "I did have a pound or two on John - all proceeds are going to party funds, and to Moira [his wife]."
The loss of such a safe seat in his native Scotland is another serious blow to the leadership of Mr Brown, and has prompted questions about how long he can remain in Downing Street.
The prime minster has insisted he was "getting on with the job" following the result, and would focus on steering Britain through tough economic times.
Des Browne, Defence Secretary and Secretary of State for Scotland, said he was convinced Mr Brown remained the best man to lead both the party and the country.
He added: "In Gordon Brown we have a leader of our party and our country who is uniquely well-placed to take us through these difficult economic times.
"Successfully he has led us through two economic shocks in the last decade and I believe he is uniquely, and I used that word advisedly, skilled to do so again."
Mr Browne said all senior figures in the party bore "a degree of responsibility" for the result, and admitted: "The people of Glasgow East sent us a clear message. We will examine what that message means and we will respond to it."