Scottish First Minister Nicola Sturgeon has warned David Cameron's successor it would be "unacceptable" for Westminster to veto a second referendum on independence in the wake of the UK's Brexit vote.
Ms Sturgeon said Scotland had voted "overwhelmingly" to stay part of the European Union and her priority is now to have talks with Brussels with the aim of keeping the country in the EU.
No talks have taken place as yet, she said, but added she would be doing so "in the next few days".
But she stressed leaving the EU - as the UK voted to do by 52% to 48% - would have "deeply damaging and painful consequences" for the country.
While the UK as a whole voted to leave the European Union last Thursday, Scots voted by 62% to 38% in favour of staying in - a result which prompted the First Minister to make clear that a second independence referendum is now "very much on the table".
She told ITV's Peston on Sunday programme: "If the Scottish Parliament votes to have another referendum in circumstances where that is the only thing we think we can do to protect our interests then frankly it is inconceivable that a Westminster government, who have thrust this situation upon us, would seek to block that, and I would seriously caution any prime minister, present or future, against doing that.
"It would be completely democratically unacceptable."
She hit out as two new polls showed a majority in favour of Scotland leaving the UK.
A Panelbase survey for the Sunday Times in Scotland found that when "don't knows" were excluded, 52% of those likely to vote would back independence, with 48% in favour of continuing as part of the UK.
A total of 626 people were questions for the research, which was conducted on Friday and Saturday, after the European referendum result was declared.
An online poll by ScotPulse - which is not a member of the British Polling Council - for the Sunday Post put support for independence higher than that , saying 59% would vote Yes in a second independence referendum, 32% would vote No and the remainder of the 1,600 sample were undecided.
Earlier, the SNP leader told BBC's Andrew Marr Show: "My challenge now as First Minister is to work out how I best protect Scotland's interests, how I try to prevent us being taken out of the EU against our will with all of the deeply damaging and painful consequences that would entail.
"If it is the case that looking again at the question of independence becomes the only way in which we can protect Scotland's interests, then that is a debate and a conversation and a decision that the people of Scotland have a right to take."
The SNP's manifesto for May's Holyrood election said the Scottish Parliament should have the right to hold another vote on independence if there is a "significant and material" change in the circumstances from 2014, when the previous vote was held.
Ms Sturgeon stressed that another referendum "is not going to be a re-run of the 2014 referendum", adding that the "context and circumstances have changed dramatically".
She said: "The UK that Scotland voted to remain within in 2014 doesn't exist any more and this is a case of how do we best protect the stability and the interests of Scotland."
The First Minister continued: "The Scottish Cabinet met yesterday and I'm not suggesting for a second that the path ahead is without complexity or it is easy. The Scottish Cabinet has decided and made clear that in the days, weeks and months to come we are going to seek discussions with the European institutions, with other member states, to explore all options for giving effect to the democratic will of the Scottish people.
"That is how I'm going to proceed and my guiding principle is the best interests of Scotland, protecting what Scotland voted for."
She added: "We're in unchartered territory, not because of choices Scotland has made but because of choices that have been made elsewhere."
Ms Sturgeon said: "I have a job to do to protect Scotland and to negotiate the best way forward for Scotland. I look on at what's happening in Westminster just now with a sense of utter despair on behalf of people across England and other parts of the UK, as that vacuum of leadership, both in the Tories and Labour, develops.
"But what I'm absolutely clear about is there is no vacuum of leadership in Scotland, as First Minister I'm going to do everything I possibly can to prevent Scotland being taken out of the European Union because the consequences of allowing us to do so would be devastating."