Ms Sturgeon wrote to the Prime Minister in a joint letter with Welsh First Minister Mark Drakeford, urging all international travellers to be required to self-isolate for eight days, and take a PCR test on day two and day eight of their arrival.
Anything other than a four-nation approach would be “ineffective”, Ms Sturgeon said.
But Downing Street has rejected this request, and has not convened an urgent COBRA meeting as asked by the First Ministers.
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A spokesperson said the UK Government’s current approach is “proportionate” and further restrictions would negatively affect the travel industry.
They told journalists: “We believe that the approach we’ve taken is the proportionate one to the evidence that we currently have available about this variant.
“Introducing further isolation requirements and testing requirements would have a detrimental affect on the travel individual industry and indeed those who are planning to go travelling
“So our response needs to be balanced based on what we know currently about this variant. We’re taking a precautionary approach we believe it’s responsible and proportionate.”
Ms Sturgeon said anything other than a four-nation approach to international travel will be “ineffective”.
“As we know from earlier stages of the pandemic, with so many people travelling to Scotland and indeed to Wales via airports in England, anything less than a four nations approach to requirements like this will be ineffective so we hope that a four nations agreement can be reached,” she told a Covid-19 briefing on Monday.
The First Minister refused to say what action the Scottish Government would take if Boris Johnson did not agree to tighter travel restrictions.
“We will continue to wait and see what the response is to that and hopefully we’ll have some positive discussions,” she said.
Under current rules, passengers arriving in the UK from 4am on Tuesday will be required to take a PCR test by the end of their second day from entry and isolate until they receive a negative test.
Ten southern African nations have also been added to a four-nation red travel list.