An independent Scotland would look to strengthen its "strong and enduring" relationship with the US, the External Affairs Secretary has told an audience across the Atlantic.
During a speech in Independence Hall in Philadelphia - where the American Declaration of Independence was signed on July 4 1776 - Fiona Hyslop stressed the "deep and strong" links the two countries share.
If Scotland leaves the UK, this "independence must inevitably go hand in hand with interdependence", she said.
An independent Scotland would seek to be a "full and equal partner" in international organisations such as the United Nations, European Union and Nato.
Ms Hyslop was invited, by the Descendants of the Signers of the Declaration of Independence, to make the speech about next year's referendum on Scotland's future.
She said she hopes that "in the not-too-distant future, I will be able to reciprocate by inviting you to Scotland to mark our very own independence celebrations".
A Yes vote in the referendum would "open the door to strong, new relationships with our neighbours and trading partners".
She said: "The people of Scotland have benefited from being citizens of the EU for almost 40 years and are set to continue to do so. Scotland's relationship with the rest of the UK will shift from a political union to a social one, a partnership of equals.
"We recognise of course that in the modern world, independence must inevitably go hand in hand with interdependence. That's why an independent Scotland would seek to participate as a full and equal partner in international organisations such as the United Nations, the EU and Nato."
Ms Hyslop, taking time out from a family holiday in the US to make the speech, argued that "America can claim some credit for Scotland's success".
She said: "The USA is our single largest overseas investor and our biggest overseas export market. Americans account for the largest number of overseas students studying at Scotland's universities and more Americans visit Scotland than from any other overseas nation.
"It goes without saying therefore that and independent Scotland would be keen to maintain and strengthen our strong and enduring relations with the United States."
She drew on links between the US Declaration of Independence and the Declaration of Arbroath, made in 1320.
"The bonds of kinship and friendship between Scotland and the USA are deep and strong. They stem not just from that common heritage but from shared history and shared values.
"Many scholars, here and elsewhere, recognise that the Declaration of Arbroath, signed in Scotland on 6th April 1320, influenced the founding fathers who crafted the US declaration. These two documents share common sentiments, values and aspirations for our two nations."
She told the audience that "just as America pursued its own particular journey towards independence in 1776, for its own reasons, so Scotland is continuing on its journey" with next year's referendum.
"Some 300 years after the Act of Union of 1707, Scotland is engaged in a national conversation about our constitutional future.
"On September 18 2014 the people of Scotland will be asked, in a referendum, to answer a straightforward question, the most important that we've had to decide in over 300 years: Should Scotland be an independent country?
"Independence is not a departure from, but the logical continuation of the devolution journey that Scotland began in 1997. And if Scotland votes Yes next September, independence will be accepted as the normal state of affairs for our country just as quickly as our devolved Scottish Parliament established in 1999 has become an established part of life in Scotland."
Scottish Conservative chief whip John Lamont said: "No doubt the American audience were as perplexed by SNP separation assertions as the majority of Scots are.
"Yet again we hear these assumed memberships a separate Scotland will be a part of, like the UN and EU - yet they haven't even asked.
"Perhaps the most surprising part of the speech is she didn't demand a seat in Congress for an independent Scotland."
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