The Scottish National Party has claimed that Gordon Brown is "caving in to pressure" to concede more powers to the Scottish Parliament.
It follows the prime minister's speech at the CBI dinner in Glasgow in which he indicated that he favoured enhanced financial powers for Holyrood.
Mr Brown said the Union was key to the economy but indicated the prospect of greater financial accountability.
Mr Brown's aides denied this was a concession to Nationalist pressure.
Speaking to the dinner on Thursday night, Mr Brown said there was a risk of waking up and finding the benefits of the Union had been thrown away.
But he said there was not "unthinking opposition to change".
Referring to the Calman Commission, which was set up to review devolution, the prime minister said: "The Scottish Parliament is wholly accountable for the budget it spends, but not for the size of its budget.
"And that budget is not linked to the success of the Scottish economy and that's why we've asked Calman to look carefully at the financial accountability of the parliament."
Scotland's Finance Secretary John Swinney told BBC Radio Scotland's Good Morning Scotland programme that he "welcomed where the prime minister had arrived at in his speech".
He added: "He [Gordon Brown] has quite clearly shifted very important ground from where he was last year.
"Last year he said there should be no increase in the powers of the parliament.
"He is now accepting that Holyrood needs more financial power and that is a very welcome step forward."
Mr Swinney said Mr Brown had "caved in" to the pressure from the SNP and the rising support for his party.
First Minister Alex Salmond claimed Scotland's message was getting through "loud and clear to the Downing Street bunker".
"With the Glenrothes by-election around the corner, Gordon Brown is caving into pressure from the SNP and the people of Scotland," he added.
"Just as SNP success forces the prime minister to take action on the economy and energy, so it is also ensuring that Scotland's parliament will move forward to meet the aspirations of the Scottish people."