The First Minister wrote on Twitter: “The scenes from the Capitol are utterly horrifying.
"Solidarity with those in on the side of democracy and the peaceful and constitutional transfer of power.
"Shame on those who have incited this attack on democracy.”
SNP Westminster leader Ian Blackford pointed the finger firmly at outgoing US president Donald Trump, tweeting: “Put simply this is an attack on democracy. We stand with our American friends in supporting the rule of law.”
He added: “The end of @realDonaldTrump Presidency cannot come quick enough. What a legacy the events of today are to his time in office. Shameful, shocking an affront to democracy.”
The riots in Washington escalated as law makers in Capitol Building were asked to stay in their offices and keep away from external windows and doors.
Social media is awash with images and videos show rioters inside the building and inside the house itself.
An armed stand off between police and rioters took place in the entrance hall, and later, a woman was removed from the building on a stretcher having allegedly been shot in the neck.
Mr Trump tweeted: “I am asking for everyone at the U.S. Capitol to remain peaceful. No violence! Remember, WE are the Party of Law & Order.”
Former Scottish Conservatives leader Ruth Davidson was among other UK political figures to react on social media, posting on Twitter: “This is insane.
“I love America. I did part of my degree in American History. I have sat in that gallery.
"I would never have believed a mob could be allowed to storm the Capitol building. Certainly never in the name of a President who refuses to condemn. Utter insanity.”
Scottish Labour leader Richard Leonard added: “Appalling scenes from Washington tonight.
"Make no mistake, this assault on democracy is the result of the demagogic actions of Donald Trump.”
Labour MP Ian Murray threw his support behind incoming US president Joe Biden, posting: “Why @JoeBiden will be a force for good in the world.
‘The words of a President matter, at best they can inspire at worst they incite’ 14 days until the worst president in history exits the stage. He leaves with no dignity.”