The First Minister’s call followed Scotland-London firm LNER admitting it had wrongly told passengers it had reached a deal with Transport Scotland to end passenger separation in line with such easing of Covid restrictions in England yesterday.
Ms Sturgeon said: “I am very clear on the legal intention of the regulations.
"It is a statutory requirement that those carrying on a business or providing a service take measures to ensure, as far as reasonably practicable, that a 1m distance is maintained."
She said she asked Scottish Government lawyers to see if the regulations needed to be tightened to ensure they covered trains.
However, she added: “The intention is clear, and I would expect companies operating in Scotland to follow the law in Scotland, and indeed to follow the guidance that is in place in Scotland, even if it is not contained in statute.
"That is, in my view, what the public would expect.
"After a bit of prevarication or controversy yesterday, I’m pleased, and would thank LNER for making clear that they intend to do that.
"I would certainly encourage all cross-Border services, when you are operating in Scotland, it is the law and the guidance that applies in Scotland that you should be following.”
LNER said it was now "reviewing our approach to social distancing” on cross-Border services after the 1m distancing requirement was scrapped by the UK Government on trains in England.
LNER had emailed passengers: "Whilst social distancing guidance remains in place in Scotland, we have reached an agreement with Transport Scotland that LNER will operate under English guidance."
However, the UK Government-run firm has now admitted the reference to a deal was incorrect.
An LNER spokesperson said, “We are reviewing our approach to social distancing onboard our Anglo-Scot services.
"We are continuing to provide an enhanced cleaning programme onboard our trains and at our stations as well as reminding customers to wear a face mask, unless exempt.
"We are also using our reservation system to prevent overcrowding and our website to continue to inform customers which are our least busy and busier services, to enable people to plan ahead and travel in confidence.”
Two other cross-Border operators said passengers should continue to follow Scottish Government regulations.
A spokesperson for CrossCountry said: “In England, social distancing restrictions are no longer in place on board our services, which is in line with government guidelines.
"Scotland still has a social distancing rule of 1m in place.
"However, there is acknowledgement that on some crowded services, 1m physical distancing may prove difficult.
"Face coverings also remain mandatory in Scotland for the time being and we make frequent announcements to inform our customers.”
An Avanti West Coast spokesperson said: “We are asking our customers to please respect others and, unless exempt, wear a face covering in crowded spaces throughout their journey.
"Onboard announcements will be made on our services to Scotland upon departure from Carlisle to advise customers of guidelines for Scotland, and give them the option to move seats to comply with social distancing guidelines if appropriate.”