In a statement, Mr Livingstone said: “Terrible incidents such as we have seen today are, thankfully, very rare in Scotland. This event has understandably shocked the people of Glasgow, and indeed, the whole country.
“My thoughts and very best wishes are with those who have been injured and their families, including our colleague constable David Whyte who was seriously injured in the course of doing his duty. I offer my personal support to all those affected.
“Officers have once again run into danger to protect their fellow citizens. Their professionalism as police officers was outstanding. I pay tribute to their bravery, selflessness and commitment to protecting the public.
“I briefed the First Minister and the Prime Minister earlier today on the circumstances and advised them both that we are not treating the attack as a terrorist incident.
“It is essential enquiries are now carried out to establish the full circumstances and all speculation must be avoided.”