Lord Robertson said independence could threaten the stability of the wider worldThe former secretary general of Nato has said that Scottish independence would be cataclysmic for the West in an era of international turmoil.
Speaking in the US, Lord Robertson said a "debilitating divorce" after a "Yes" vote in September would threaten the stability of the wider world.
He said he believed the American administration was worried about the possibility of Scottish independence.
The Scottish government said the comments were "crass and offensive".
Scotland's Deputy First Minister Nicola Sturgeon said she was "shocked" by the language of the former Labour defence secretary.
Lord Roberston was speaking at the Brookings Institute where he said the US should make its views public - as should all British allies.
In a strongly-worded speech, he said: "The loudest cheers for the break-up of Britain would be from our adversaries and from our enemies.
"For the second military power in the west to shatter this year would be cataclysmic in geo-political terms."
He went on to urge "Britain's allies" to speak out and to say that an independent Scotland would "affect them as well".
Lord Robertson added: "This is not a purely domestic matter even though it's a decision that will be taken by the Scottish people.
"The Scottish people need to be conscious that they are taking a decision, not just for themselves and for future generations in a one-off vote, but that it also has an effect elsewhere and people who are affected, or think they will be affected, have every right to speak out."
A spokesman for First Minister Alex Salmond said: "Scotland can and will make a hugely positive contribution to the world as an independent country - and our referendum is a model of democracy, which was cited as such only last month by the US Secretary of State.
"It is disappointing but not surprising that Lord Robertson fails to recognise any of that in this crass and offensive speech that has absolutely nothing positive to say.
"And it is contributions like his which are turning people across Scotland in their droves away from the fear and smear tactics of the No campaign towards the positive, upbeat, optimistic message of the Yes campaign.
"Lord Robertson once claimed having a Scottish Parliament would kill demand for independence stone dead - with comments like this it is the No campaign that will continue to sink like a stone."
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