The Alba party's leader at Wesminster has criticised the "violation" of Ukraine while calling for Russia’s "security interests" to be part of any solution.
In a lengthy statement, Neale Hanvey MP also cautioned against NATO expansion eastwards - a key gripe of Vladimir Putin.
It came after the Russian president ordered troops into two regions in eastern Ukraine, after recognising them as independent states.
The invasion was condemned by the international community and Prime Minister Boris Johnson is set to announce sanctions.
Putin has tried to justify his country’s action by claiming that Ukraine could join NATO and pose a threat to Russia.
Although politicians in mainstream political parties in Scotland have slammed the Russian aggression, some observers have been waiting for the reaction of the pro-independence Alba.
Salmond, who founded the pro-independence party after leaving the SNP, hosts a programme for the Kremlin-backed RT broadcaster.
Critics have described RT’s coverage of the Ukraine invasion as propaganda and called on Ofcom to revoke its license.
Hanvey, a former SNP MP, said of the overnight events: "ALBA condemns the violation of Ukraine’s sovereignty and territorial integrity. Russian recognition of the Donetsk and Luhansk as independent republics is a serious breach of the Minsk protocols.
"This is a moment for cool heads and careful words if we are to avoid a Cuban Missile Crisis in reverse.
"We need an intensification of diplomatic efforts, dialogue and restraint. A hot war in Europe could quickly spiral with catastrophic consequences stretching far beyond the economy."
He also called for action to be taken against Russia: “Sanctions can and should be introduced and in terms of dirty London money are long overdue but they must be carefully targeted if they are not to be counterproductive to our own economic security.
“The spike in energy prices is already being felt in every household across these islands.
However, he broadened his analysis to reference issues that have separately been raised by Russia.
He said: “The task is, as it has always been, how to ensure respect for Ukraine’s rights as an independent country including the recognition of the rights of the Russian speaking minority as stated in the Minsk accords.
“All of which has to be reconciled with Russia’s own security interests. That requires our acceptance that assurances were offered in the 1990s about NATO expansion eastward which have not been kept.
“The emphasis at this critical moment should be on de-escalation not escalation. At the end of the day conflict can only be resolved through dialogue and negotiation.”
Alba’s statement is in stark contrast to the tweets of SNP First Minister Nicola Sturgeon.
She retweeted a scathing comment by journalist George Eaton, who wrote: “Vladimir Putin is an unashamed imperialist and chauvinist and progressives should condemn him to the dustbin of history.”
She also retweeted Russia expert Michael McFaul: “When you describe Russian soldiers invading Ukraine right now as "peacekeepers", even when you use quotation marks, you are using language that Putin wants you to use. Call it what it is -- an invasion.”
Stewart McDonald, the SNP’s defence spokesperson, criticised RT being allowed to broadcast in the UK: “Russian disinformation is central to the Kremlin's case for, and execution of, war. RT is a fundamental and strategic part of that effort and has to be treated as such - it is not an informative news source in the traditional sense that we understand.
“Quite why it is allowed to continue posing as one, whilst Ukrainian citizens face a new wave of bloodshed baffles me.”
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