The United Kingdom should be "pulling together, not pulling apart", the Prime Minister will insist today.
David Cameron will cite the UK's success at last summer's Olympics and the efforts of British soldiers in World War Two as he calls on people in Scotland to remain part of a "prosperous, compassionate Britain".
A referendum on independence next year will decide if Scotland remains in the UK.
Alex Salmond's Scottish National Party administration at Holyrood is making its case for the country to become independent.
Mr Cameron will use his speech at the Scottish Conservatives party conference in Stirling to set out his vision for Scotland's place in the UK.
He will argue there is no challenge the country is facing to which "breaking up Britain is the right answer".
The UK's history "has always been one of shared endeavour", with different countries "proud in our individual identities but working together for a common good", Mr Cameron is expected to say.
"We saw it when our soldiers fought together under one flag on the beaches of Normandy. We saw it when our doctors came together to build our NHS. We saw it in the scientific breakthroughs that we made together: from the television to penicillin. And we saw it last summer as athletes from around Britain, no matter where they were from, draped themselves in one flag."
But there is "still so much more to come", he will say, asking: "Why wouldn't we want to face the future together?
"There is simply no challenge we face today where breaking up Britain is the right answer.
"The future I see for Scotland is part of a dynamic, enterprising, prosperous, compassionate Britain; a Britain that isn't just competing in the global race but winning in the world; a country where we are pulling together, not pulling apart."
Mr Salmond made a fresh call for the Prime Minister to take part in a TV debate with him before the independence referendum on September 18 next year.
"Given that David Cameron's Government at Westminster is clearly leading the No campaign, he should be prepared to engage in a referendum debate with me about Scotland's future," the Scottish First Minister said.
"The Prime Minister is the most senior elected politician arguing for a No vote. If he wants to be part of the debate, he has an obligation to take part in a debate so that the people of Scotland can judge our respective cases.
"I am confident that the people of Scotland will choose Yes. It is time for David Cameron to step up to the plate."
The SNP leader also called on Mr Cameron to apologise for the "scaremongering" by those opposed to independence.
This "negative approach" came from "the top of the UK Government down, and permeates the entire No campaign".
The First Minister said: "It is time for the No campaign to draw a line in the sand under their fears and smears about Scotland, and fulfil their pledge to pursue a positive campaign based on reality.
"The Prime Minister should do that by apologising for his part in peddling claims that have been proven to be utterly wrong, and he has a perfect opportunity to do so at the Tory conference in Scotland."
Scottish Conservative leader Ruth Davidson has faced criticism from her own party over her U-turn on devolving more powers to the Scottish Parliament.
Speaking to the BBC's Good Morning Scotland she defended the lack of a debate on the issue at the conference and denied that she was afraid of the party membership.
Ms Davidson said: "To have a debate on the conference floor you need a motion to debate to, you need to have concrete proposals there. We do not have anything back from the Strathclyde Commission yet because we've only just set it up."
She denied that she was "hiding behind" the commission headed by Lord Strathclyde that was set up to examine the issue.
"When he comes back with concrete proposals they will be taken to the membership and that is the proper way and manner and process in which this should be established," she said.
Defending her position as leader, she said: "I was elected by the whole of the Conservative Party, the first leader of the whole Conservative Party in Scotland, not just the MSP group, and the first leader to be elected one member one vote to have a mandate across the whole party."
She added: "Yes, I think that the constitutional debate over the last couple of years has changed in Scotland. We're trying to adapt and what I wanted and what I have said right from the beginning is I want a stable devolved settlement within the UK so Scotland stays part of our United Kingdom because I'm a passionate supporter of the UK.
"Yes there are a wide range of views across the party. I'm trying to accommodate people from different sides of the party to be involved in that debate.
"There is a structure that has been set up under Lord Strathclyde in order to discuss it in a mature fashion and come to a set of proposals that not just meet the aspiration of the people of Scotland but also gives us a devolved settlement that's stable."