Her intervention came as she announced the number of daily coronavirus cases had increased to 1,433 and fatalities to 50, the highest death total since May 20.
She said it was too soon to know whether this was an anomaly or the start of a new surge following a 22 per cent drop in case numbers over the previous week.
Ms Sturgeon has warned that some local authorities could be “moved up a level” in her five-tier system when it is reviewed next week, including to the highest Level 4, which is the equivalent of almost full lockdown.
The First Minister last week placed 19 of Scotland’s 32 local authorities in level 3 of her new five-tier system, which started on Monday.
They included councils across the Central Belt such as Edinburgh and Glasgow, along with Dundee, Stirling and Ayrshire. Residents in these areas are advised not to make non-essential journeys beyond their council areas.
People across all council areas are also advised not to travel south of the Border, with England going into a second lockdown on Thursday.
Appearing before Holyrood’s Covid-19 committee, Ms Sturgeon said yesterday: “We are actively considering whether we give a legal underpinning in future weeks to these travel restrictions and I’ll probably say more about that at the review point next week.
“But whatever approach you take to travel restrictions, it relies on people abiding by them.”