Nicola Sturgeon has asked people not to protest on the Scotland-England border, saying it is not "sensible or helpful".
The first minister said protestors who displayed a "keep Scotland Covid free" banner at the border with England on Saturday "do not speak for me".
Ms Sturgeon has refused to rule out a quarantine system for people coming to Scotland from other parts of the UK.
However, she stressed this was "about public health", not "whether people in England are welcome in Scotland".
There are currently no plans to impose quarantine or any other kind of restrictions on travellers from the rest of the UK into Scotland, and there has been no formal discussion on whether they should be introduced.
But there has been an escalating row between the Scottish and UK governments over the issue, with Prime Minister Boris Johnson saying "there is no such thing as a border between Scotland and England" and Ms Sturgeon hitting out at "absurd and ridiculous political statements".
On Saturday, a small group of protestors gathered at the side of the A1 road at the border, wearing protective overalls and encouraging people to "stay out" of Scotland.
The group were widely criticised both by Scottish government figures and opposition politicians, with Justice Secretary Humza Yousaf tweeting that "these morons don't represent the Scotland I know and love".
Police Scotland said officers had been called to the scene and had given "suitable advice" to the protestors.
When questioned about the matter at her daily coronavirus briefing, Ms Sturgeon said she agreed with Mr Yousaf.
She said: "The people who protested at the border did not speak for me, they were not there on my behalf or communicating a message that I endorse in any way. I would emphatically say I do not endorse that."
The first minister added: "This is not a question about whether people in England are welcome in Scotland - of course they are, just as people in Scotland are hopefully welcome in England. It's about public health and I will take decisions based on protecting the people of Scotland if there is a risk to public health.
"That is not political or constitutional and it is certainly not based on any desire to keep English people out of Scotland."
In response to a further question, she added: "I don't approve of the protests, and I would ask people not to protest on the border because I don't think it is a particularly sensible or helpful thing to do.
"I can't be clearer than I have been - the SNP is an open and welcoming party and Scotland is an open and welcoming country, and that kind of protest is not something I condone or endorse in any way, shape or form."
Scottish Conservative MSP Oliver Mundell said it was "shameful it took a question from a journalist to force [Ms Sturgeon] to take some responsibility for stoking division and fear".
The first minister has repeatedly pointed to other parts of the world where local quarantine schemes are in place - such as in the US state of New York - saying she would be failing in her duty if she did not "consider all options" in the event of "ongoing divergence between infection rates and levels in Scotland and other parts of the UK".
At a previous briefing, she said it would be "frankly disgraceful" to turn a question of public health policy into a "standard political or constitutional row".