Theresa May has said Scotland was only able to "weather the storm" of the collapse in North Sea oil revenues because "of the UK's broad shoulders".
The Prime Minister said Scotland's public services emerged "unscathed" from the crisis because of the support provided by being in the United Kingdom.
She also accused the SNP of presiding over a nation where many are "only just" getting by while "those at the top seem to flourish with ease".
She made the comments in a Facebook statement pitched at wooing Scottish voters ahead of the Conservative Party conference this weekend.
Mrs May said: "It has become even clearer in recent months that the union which really matters to Scotland's future is its union with England, Wales and Northern Ireland, our centuries-long ties of people, trade, history, culture and values.
"The fall in oil prices demonstrates just how crucial that relationship is financially: Scotland was able to weather that downturn because of the UK's broad shoulders.
"Tax revenues from the North Sea collapsed but funding for Scottish public services remained unscathed.
"That is how our union works: we share each other's successes when times are good, and shoulder each other's burdens when times are tough."
Scotland's share of North Sea oil revenue fell by 97% in the past financial year, reigniting the debate over whether an independent Scotland could afford to finance itself.
There have been growing calls for another independence referendum following Britain's decision to leave the EU, which Scotland voted overwhelmingly against.
Mrs May stressed the Conservatives "hold dearly the precious bond" of the UK and will "fully engage with" the Scottish Government as they draw up the UK's Brexit negotiating position.
She also reiterated her commitment to making a success of Brexit, adding: "As we strike that deal, we have an exciting chance to forge a new role in the world.
"Scotland's status will not be diminished by that; it will be enhanced.
"We will go out into the world with the aim of being a leader in global free trade, one that makes the most of our advantages, from the financial expertise of Edinburgh to the shipbuilding prowess of the Clyde and the globally-renowned food-and-drink produce of Scotland's countryside."
The new Prime Minister again sought to appeal to hard-working but financially-squeezed voters who, she said, felt they had been "ignored by politicians, at Westminster and Holyrood, for too long".
She added: "These are the people who get up early, put in the hours, play by the rules yet still feel like the wind is against them. They're getting by - but only just.
"Meanwhile, those at the top seem to flourish with ease and often flout the rules with impunity.
"That feeling is as strong in Scotland as it is anywhere else in the UK, and after nine years as the establishment party in Scotland, the SNP needs to accept its share of responsibility."
She promised to restore fairness to society and "trust to our political system".
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