News of the incident emerged as Chief Constable Phil Gormley and other senior officers took part in a meeting of the Scottish Police Authority (SPA) in Stirling.
Mr Gormley, who appeared to be checking for updates on his phone during the meeting, said there would be an “uplift” in armed officers, who would be deployed across the country.
Deputy Chief Constable Johnny Gwynne left the meeting to help coordinate Police Scotland’s response from the multi-agency crime campus at Gartcosh, North Lanarkshire.
Mr Gormley said: “We’re putting in place some reassurance measures. We have increased armed patrols around key sites in Edinburgh. There will be armed patrols around key locations in Scotland.
“At the moment, there’s no information to suggest this is anything other than an isolated attack.
“We’ve uplifted and deployed a number of armed officers into key places and we’re working very closely with colleagues in London to understand exactly what has happened and what we need to do to support them and keep Scotland safe.”
Last year Police Scotland increased its armed officers by a third following terror attacks in Paris and Brussels.
It followed comments from the Scottish Police Federation that the force was “woefully under-equipped, under-resourced and under prepared” for a similar attack.
Last night, Calum Steele, general secretary of the SPF, said: “Events in London serve as a sad reminder of the reality of the threat facing the UK.
“Sadly, they also serve to remind us of the dangers faced by police officers every single day.
“Our thoughts go to all who have been killed and injured, and especially the family, friends and colleagues of the police officer who sadly lost his life.”