Nicola Sturgeon made the pledge as she opened the Teenage Cancer Trust's ninth international conference in Edinburgh.
Sturgeon: Scotland 'Key To Preventing Brexit'
Nicola Sturgeon claims Scotland could be key to preventing Britain voting to leave the EU in next week's referendum.
The First Minister warned polls showing a lead for Brexit should be a "wake-up call'' and said Scottish voters could "make a difference''.
She said: "With 10 days to go until the referendum, the result of this vote is in the balance.
"Polls showing a lead for 'Brexit' should act as a wake-up call to anyone who assumed that it would be an easy win for the Remain side.
"But I still believe there is a majority for an 'in' vote across the UK - especially if everyone who believes in our place in Europe turns out to vote.
"And Scotland's voice could help to make the difference in this contest, especially if the result is as close as some polls suggest.
"While I take nothing for granted, I believe Scotland will vote strongly to stay part of Europe - and that Scottish voters could increase the margin of victory for Remain.''
Meanwhile, the Scottish Green Party plans to publish a letter to voters in Scotland on Monday, urging them to vote to Remain in the EU.
The party's co-convener, Maggie Chapman, criticised the "casual racism'' of the referendum debate "dominated by a right-wing story that blames the EU for all our problems and says we need to shut our borders''.
She added: "Today we appeal to every voter in Scotland to vote Remain and help to build a better Europe.
"It's only by working together with like-minded people across the EU that we can make the changes that Europe so desperately needs.''
Tom Harris, director of Scottish Vote Leave, said: "I think the Scottish political establishment will be in for a shock if they think we will believe David Cameron's scaremongering.
"If we leave the EU we would secure more powers for the Scottish Parliament, we would be able to have control over our borders, and control over vast sums of money. If we leave, Scotland would be able to take back control over our future
"SNP voters will be wondering why they're being asked to vote against more powers for Scotland, and why they're being asked to continue being governed by an unelected, unaccountable political elite in Brussels which threatened Scotland during the independence referendum.''
The 25 year old from Scotland was found dead on Saturday.
Major cities across Britain are becoming home to "hipster hotspots'' - pushing up house prices strongly in places such as Bristol, Manchester and Edinburgh as well as in London - research has found.
The Convention of Scottish Local Authorities (Cosla) has said that any more cuts to local government funding will result in "severe consequences'' for jobs across the country.
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