The education secretary told MSPs that she had held a meeting with police and local authorities.
“As a parent and as a constituency MSP I understand just how concerning this will be for parents, for pupils, for carers and for school staff,” Mairi McAllan said.
“I would take this opportunity to repeat Police Scotland’s advice that there is nothing to suggest any threats to the public from the content of the emails.”
The cabinet secretary added there was a “considerable amount of work” ongoing by Police Scotland and partners across the UK to “understand the motivations and the individuals behind this”.
Most local authorities contacted by BBC Scotland said schools were operating as normal but some confirmed pupils had been evacuated.
More than 300 calls were made to police when a similar message was sent to schools around the country on 19 October.
In many areas, pupils were off due to half-term holidays.
On Wednesday the majority of schools in Dumfries and Galloway received the email and some were evacuated as a precaution.
A spokesperson for the local authority said: “Each school community/setting is unique and as such has its own way of supporting and reassuring learners and staff.
“We also know that local police have attended some school settings in a community capacity to assist and reassure.”
In Edinburgh Queensferry High School was evacuated and pupils were sent home.
Highland Council confirmed a number of its schools “made the decision to activate their emergency protocols”.
Local authorities in Glasgow, Edinburgh, East Lothian, Aberdeenshire and Orkney also confirmed their schools received the message.
In Northern Ireland, the Education Authority (EA) said the “message has similarities with a bogus threat sent last month” which was treated as a hoax by the (PSNI).
The Police Service of Northern Ireland said the email originated from outside the UK.
Italian reports said 280 school head teachers had received threats in recent days. Italian Prime Minister Giorgia Meloni has called a meeting of top ministers and intelligence chiefs over the issue.
