The Conservative MP was stabbed to death at his constituency surgery in Leigh-on-Sea, Essex, on Friday.
A 25-year-old man was arrested on suspicion of murder, which police are treating as a terrorist incident.
In a letter addressed to Scottish MPs and MSPs, Police Scotland’s Chief Constable, Iain Livingstone, said four virtual sessions had been scheduled with specialist officers.
The force has also distributed new guidance to Scottish councillors through local government body Cosla, but insisted there was "no specific threat to Scotland”, according to the BBC.
Mr Livingstone said Sir David’s death had "rightly given rise to wide-spread shock and distress".
"I recognise this comes at short notice, however consider it important to extend this invitation as a matter of priority.
"I hope that you are able to join the security briefings and, of course, if you have any specific personal concerns please raise them with your own local area commander."
Mr Livingstone added: "While such attacks are rare, they are shocking and utterly unacceptable. It is vital our elected politicians are able to carry out their duties safely.
"You have my full support in delivering your public service."
“I would urge you to use 999 in an emergency if you at any time feel under threat.
"I wish you and your families well and thank you for the continued political leadership and public service you provide across the country."