Speaking at a hate crime conference in Glasgow, the Police Scotland leader said uniform patrols at Edinburgh and Glasgow airports will be increased to reassure the public.
Mr Gormley did not discuss any potential threats to Scotland but asked the public to be “sensibly vigilant”.
Lord Advocate Frank Mulholland said he would personally lead a team to ensure any reprisal attacks against certain communities are dealt with.
“What they want is to polarise different communities and set them against each other,” he said.
“After the Paris attacks we looked at whether or not there was any increase in hate crime and we found a spike in crimes against our Muslim communities and Jewish communities.
“It was small numbers but something that we were dedicated to take action against and thankfully after a few weeks it reduced.
“We will do the same given events in Brussels and will look at incidents of hate crime directed at all our communities in Scotland.”
First Minister Nicola Sturgeon said she had spoken to the Belgian Ambassador “to convey Scotland’s sympathy, support and solidarity”.
She said: “While the UK threat level has not changed and there is no specific threat in Scotland, police patrols in place at airports and rail stations have been increased to provide reassurance.”