The SNP leader admitted the word "national" could be "hugely problematic".
Parliament Police To Continue Carrying Weapons
Police patrolling outside the Scottish Parliament will continue to be armed after a review of security.
Officers armed with Tasers were deployed outside Holyrood after the terrorist attack at Westminster in March.
Security was upgraded to officers with firearms following subsequent terror attacks in Manchester and on London Bridge.
Police Scotland Assistant Chief Constable Bernard Higgins said a review of parliamentary security had been completed and a report provided to the Parliament.
He said: "In support of one of the recommendations contained in the report we have made the operational decision to maintain armed police officer presence at the Scottish Parliament on an ongoing basis.
"This is an operational contingency to provide protection and reassurance to the public and staff who attend at the Scottish Parliament. This will hopefully never be needed but demonstrates our ability to respond to any eventuality.
"This decision is proportionate and justified and is in line with the operational response at other devolved legislative assemblies in the UK, and will be reviewed on a quarterly basis in line with our other armed policing standing authorities.''
In an email to MSPs and staff, Holyrood chief executive Paul Grice said the move was a precautionary step.
"While the advice is that there is no specific threat to the Parliament at this time, their clear rationale is to provide an enhanced visible deterrent and ensure the safety of all those who work in and visit Holyrood,'' he said.
"Overall, the review found the Parliament building already has in place a substantial number of effective security features. It also noted the established good practices which are in place in relation to security management at Holyrood.
"However it is important we continue to work with partners to ensure our security measures remain appropriate.''
Police patrols will also be extended to cover the area inside the public entrance where visitors pass through security.
Last year it was announced that the number of officers attached to armed response vehicles in Police Scotland would increase by a third to 365.
Mr Higgins added: "All communities in Scotland benefit from the protective policing offered by armed response officers and I am currently reviewing how all our armed response officers are deployed across the country to ensure that they are used to their maximum benefit.''
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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