The idea of quarantining visitors entering Scotland from other parts of the UK is "astonishing and shameful", Prime Minister Boris Johnson has said.
First Minister Nicola Sturgeon has said "all options" must remain open should coronavirus infection rates "diverge" between different parts of the country.
However both leaders said there had been no talks about the potential for new travel restrictions to be imposed.
Ms Sturgeon said it would be "frankly disgraceful" to politicise the issue.
She said if advisors told her that a quarantine rule would be "a necessary measure to protect people" then she would be "failing in my duty not to consider it".
There are currently no plans to impose a quarantine or other restrictions on travellers entering Scotland from other parts of the UK, but Ms Sturgeon has refused to rule the idea out as she pushes to effectively eliminate coronavirus north of the border.
She said that if there was an "ongoing divergence" between levels of the virus in different parts of the UK, then "from a public health perspective we have to be able to consider all options to try to stop a resurgence of infection in Scotland".
The first minister has pointed to other parts of the world where local quarantines are in place, such as in the state of New York and between some regions of Germany.
Public health, not politics, must drive decisions on COVID. I’m sure the Governor of New York (below) isn’t being political in imposing quarantine on people from higher transmission US states - he’s acting to protect the people he serves from a deadly virus. https://t.co/eH2iSWoBLy— Nicola Sturgeon (@NicolaSturgeon) July 1, 2020
The topic was raised at Prime Minister's Questions, with Mr Johnson describing the idea as "astonishing and shameful".
He added: "There have been no such discussions with the Scottish administration about that, but I would point out that there is no such thing as a border between England and Scotland."
Scottish Secretary Alister Jack had earlier told MPs that Ms Sturgeon had "encouraged reckless talk".
He said: "This talk of quarantining people from other parts of the UK is disappointing, it's divisive. It's not the language we should be hearing from our first minister because it undermines the joint efforts that we've had in tackling Covid-19, and it's bad for business - especially the tourism business."
The Scottish Tourism Alliance said 70% of Scotland's tourism comes from the UK market, and that "any restrictions on domestic travel will have a significantly negative impact on the sector".
Chief Executive Marc Crothall said he knew of "a few businesses who have received inquiries from people south of the border who have become concerned about a potential quarantine and have asked for reassurance of a full refund should a quarantine come into force".
Asked about the Commons exchanges, Ms Sturgeon said she did not want to have to deal with "absurd and ridiculous political statements" while dealing with a highly infectious and potentially deadly virus.
She said it was "shameful and unacceptable" for anyone in government to politicise a public health issue, saying: "It's about how a virus spreads, not about politics or the constitution".
"I very much look forward to the day where I can have straightforward political and constitutional debate with my opposite numbers, and I will relish that as someone with very strong beliefs," she added.
"But right now I have a duty I take really seriously, to protect Scotland from this virus.
"I have no plans right now to have any consideration around quarantine for people coming to Scotland. If that changes and the advice I'm getting is that it would be a necessary measure to protect people, then I would be failing in my duty not to consider it.
"This is public health, and the fact in Scotland we are trying to turn it into a kind of standard political or constitutional row is frankly disgraceful."
Ms Sturgeon later confirmed that no talks had taken place about any potential new restrictions, saying: "I have no proposal on the table to have quarantine for people coming into Scotland from the rest of the UK, so there is nothing to discuss right now.
"If that changes - and I would not be doing my job properly, given the nature of what we're doing with right now, if I ruled things out that countries around the world are using selectively in appropriate circumstances - if I have a proposal then I will discuss that with other administrations as appropriate. We will discuss things when we have got things to discuss."
The first minister also said Mr Johnson's comment about there being no border between Scotland and England was "such an absurd statement".
She said: "If the prime minister is questioning that now I'm not sure what he'd say if I pitched up in Newcastle and tried to implement Scottish government policies there."