The 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 US 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 Institution 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."
In response to the comments, Ms Sturgeon said that given Lord Robertson's "long-standing" opposition to independence, she was not surprised.
However, she added: "On another level though I am quite shocked at these comments.
She went on: "The contribution George Robertson made last night, and particularly the language he has used to make it in, I think does a real disservice to the debate.
"I am not shouting down George Robertson, I am saying very clearly that I find his comments deeply insulting.
"He is of course the man that predicted that devolution would kill the SNP stone dead, so his predictions perhaps don't hold too much water."
Ms Sturgeon said she wanted to have a rational debate.
In a plea to the former politician, she said: "I'm not the person using language like cataclysmic and suggesting that independence would aid the forces of darkness.
"I would invite George Robertson to come back into the realms of decent and rational debate, because that is the kind of debate we should be having."