The SNP leader admitted the word "national" could be "hugely problematic".
Scottish Police Review Security After Nice Attack
Police in Scotland have reviewed security arrangements as a precautionary measure following the attack in Nice.
The force stressed there is no specific information which suggests the country is at risk, but the UK threat level remains at "severe''.
At least 84 people, including several children, were killed when a terrorist drove a truck through crowds celebrating Bastille Day in the French city.
First Minister Nicola Sturgeon wrote on Twitter: "My thoughts are with all those affected by this senseless attack on Nice. Scotland stands in sadness and solidarity with France.''
Eyewitnesses said the killer swerved the truck from side to side to kill as many people as possible as he drove for hundreds of metres along the Promenade des Anglais on the seafront on Thursday evening.
Assistant Chief Constable Steve Johnson, Police Scotland's lead officer for organised crime, counter terrorism and safer communities, said: "Following the tragic events in Nice yesterday, Police Scotland has reviewed security and safety arrangements as a precautionary measure.
"This is something we would do as a matter of course after such events and it is not in relation to any specific information or intelligence.
"Police Scotland is committed to ensuring all communities across the country are as safe as they can be and I would ask the public, especially around crowded places and transport hubs, to remain vigilant and alert, but not alarmed. If you suspect something is wrong, then report it to the police.
"I would stress that there is no specific information which suggests Scotland is at risk of attack, however the UK threat level remains at severe and our communities are not immune from the threat of an attack. That's why I would encourage people to go about their business as normal, but remain vigilant.''
He added: "I am confident that the diverse, welcoming and multi-cultural communities across Scotland will work together to ensure no individual or community feels marginalised or isolated by the actions of criminals.
"Our thoughts at this time are very much with those individuals and communities affected by the events in France.''
France was still on high alert after the Paris terror attacks last November in which 130 people were killed at sites including the Bataclan Theatre and Stade de France.
Scottish Labour leader Kezia Dugdale said: "The people of France have suffered devastation and loss in recent years that no nation should have to go through.
"Once again the thoughts and prayers of everybody in Scottish Labour and across the country are with the people of France.''
Holyrood's Presiding Officer Ken Macintosh said: "I am truly shocked and deeply saddened by the news from Nice. This was an horrific attack made all the more so by the apparent deliberate targeting of families.
"The Parliament's flags will fly at half-mast as a mark of respect for those who have lost their lives and to show our solidarity with the French people.
"I will also be writing to the French consul-general today on behalf of the Parliament to express our condolences. Our thoughts are with all those affected.''
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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