First Minister Nicola Sturgeon is due to chair a meeting of the Scottish government's resilience committee after the terror attack in London.
Six people were killed and at least 48 injured in the attack on London Bridge and in nearby Borough Market at about 22:00 on Saturday.
Three suspects were shot dead by police officers.
The main Scottish political parties have said they are suspending national campaigning ahead of the election.
A white van hit pedestrians on London Bridge, then three men got out and stabbed people in nearby Borough Market.
Police said the men were wearing fake bomb vests.
Ms Sturgeon said: "Following the horrific terrorist attack in the centre of London last night we are working closely with the UK government and Police Scotland to monitor the situation.
"Later today I will chair a meeting of the Scottish government's resilience committee.
"My thoughts are with the families and friends of those who have tragically lost their lives and with everyone who has been harmed or affected by these terrible incidents."
Scottish Labour leader Kezia Dugdale said her "thoughts and prayers" went out to the victims and their families.
"Once again our nation finds itself under attack from those who hate our way of life and seek to change us.
"But we will not allow that to happen, because the values that they hate - democracy, the rule of law and tolerance - are what make our country so special.
"It's why Britain is a beacon for other nations around the world. We will not let the terrorists win."