The First Minister said austerity, Brexit and Scotland’s ageing population meant it was time to “ask ourselves some tough questions”.
“None of us want to see our cherished public services increasingly constrained in what they can deliver.
“So with all the pressures we now face, we must consider if the time has come for those who earn the most to pay a modest amount more to enable us to do so.”
She spoke out as the Scottish Government launched a new paper setting out the role of income tax in the Scottish budget - and looking at a number of “alternative approaches”.
Ms Sturgeon stressed that these are “not at this stage firm policy proposals”, saying ministers would make their position clear when the Scottish Budget is unveiled in December.
She was also clear that the Government would “not propose alterations to income tax rates lightly”, saying any changes would have to pass four key tests, the first of which is to consider if they will help maintain the level of public services that people expect.
Also, low earners must be protected, and changes to the tax regime must make the system fairer and more progressive, and must not damage the economy.
Holyrood has power over income tax rates and bands, with Labour, the Liberal Democrats and the Scottish Greens all pressing the SNP administration in Edinburgh to increase charges to provide additional cash for public services.
Ms Sturgeon previously signalled she wanted a discussion on the “responsible and progressive” use of those powers, as the Scottish Government asked the other parties at Holyrood to set out their proposals.
Austerity measures imposed by Westminster will see the Scottish Government lose £2.9 billion from its budget over a 10-year period, SNP ministers have said - although Conservatives insist the amount of tax Holyrood gets in real terms is still rising.
Tories have repeatedly made clear their opposition to tax hikes in Scotland which would make the country the highest taxed part of the UK
Ms Sturgeon said: “Scotland now has a greater measure of fiscal control than at any time since the start of devolution.
“By far the biggest fiscal lever we have is income tax - with 30% of Scotland’s budget now coming from income tax receipts. Of course, more than 60% of Scotland’s spending power is still dependent on decisions taken at Westminster.
“With that greater ability to levy tax comes a corresponding duty to do so responsibly and in a balanced way. My Government will always do exactly that.”
She said the paper published by ministers would “help aid and inform” the debate on tax in Scotland, and added: “After rigorous, careful and considered discussion, we will bring forward policy proposals that we consider to be in the interests of the country as a whole.”
Scottish Finance Secretary Derek Mackay said: “I am seeking a well-informed and considered debate on the use of our powers, recognising that in a parliament of minorities common ground on tax must be found to secure a budget for Scotland.
“We have therefore set out alternative approaches for discussion, that we believe could better meet the four tests we have established.
“We will engage in the discussions in an open-minded and constructive manner, and as the paper makes clear, the Chancellor’s decisions on overall spending and tax policy for the rest of the UK are still critically important in determining Scottish Government funding, final decisions on tax and spend will be made in the proposed Scottish budget.”
Scottish Conservative finance spokesman Murdo Fraser made clear his party’s opposition to any tax increases that would see Scots pay more than their counterparts south of the border.
“Our position simply is that Scotland should not have higher taxes than the rest of the United Kingdom,” he said.
“As job creators and industry bodies have made clear, higher levels of taxation in Scotland will make it more difficult to grow the Scottish economy.
“This will in turn result in lower tax revenues to help pay for our schools and hospitals.
“Scotland must remain competitive. We would urge the SNP to ensure that Scotland does not become a place where we cannot attract jobs and build prosperity.”