David Cameron's New Year message sent out across the United Kingdom finished on the issue, saying: "The outcome matters to all of us, wherever we live in the UK. This is not a vote for the next few years, but a vote that could change our country forever.
"Our family of nations is at its best when we work together with shared interest and common purpose.
"This year, let the message go out from England, Wales and Northern Ireland to everyone in Scotland - we want you to stay, and together we can build an even stronger United Kingdom for our children and grandchildren."
Mr Cameron said the Coalition's resolution is to stick to the long-term plan that "is turning the country around". He said 2014 was a vital year for the economy.
The economy is turning a corner, he claimed, with businesses opening up, people getting decent jobs and factories making British goods and selling them to the world.
"That's why this year, 2014, we are not just going to stick to the plan. We are going to redouble our efforts to deliver every part of it, to benefit the whole country and secure a better future for everyone," he said.
Mr Cameron pledged the Government would keep mortgage rates low amid fears this year will see a rates hike, and "help families across Britain".
Labour leader Ed Miliband issued a tailored New Year message to Scots.
He insisted: "I believe in the UK most of all because I believe in a more just, more equal, more fair country, and I believe we can best achieve that together with the people of Scotland."
He pointed to Labour pledges to abolish the bedroom tax, freeze energy bills and tackle low pay, adding: "Scotland is rightly proud of its traditions of social justice. The SNP want to tell you that we can't achieve social justice in the UK because there is a Scotland that believes in it and an England that does not. They're wrong."