Under the new rules which came into force on Monday, people flying into Scotland from overseas will have to self-isolate in a quarantine hotel for ten days.
In Scotland these rules apply to travellers from all countries, but in the rest of the UK just those coming from 33 “high risk” countries are affected. Concerns have been raised over a possible loophole, with travellers from those countries able to enter the rest of the UK without quarantining and travel on to Scotland.
The border between the two nations is not supposed to be crossed except in the case of essential travel, but Ms Sturgeon said she “would not rule out” stricter measures.
Asked if she would consider closing the border at the coronavirus daily briefing on Monday, she said: "I don’t rule it out. I would like to have the most effective system in place here.
"I'm not sure it is the best solution to have, but if it's the only one I can put into place, then it may come to that.”
She added that she would prefer to see a cohesive approach between nations.
"Why let somebody travel across the UK before you do that?” she said.
"It would be better if we had that four nations approach, or certainly at least a three nations approach, where the border of the island that Scotland England and Wales share had the same provisions in place.”
She added: “My responsibility is to try and protect Scotland as much as possible so if it just proves impossible to do that then we have to look at alternatives, but it would be far better to try to come to a reasonable agreement on a four nations, or at least a three nations, basis.”
Ms Sturgeon said she was confident in people’s willingness to comply with these requirements rather than searching for loopholes, saying that compliance with restrictions has been “very strong” throughout the pandemic.
She added that she did not criticise the UK government’s approach.
"We all have a duty to take the decisions that we think are appropriate,” she said.