The SNP leader said Brexit and the "horror show" of the Conservative leadership contest illustrated the gap that has opened up between politics north and south of the border.
Addressing the European Policy Centre think tank in Brussels, she said: "The people of Scotland have to have a choice before it's too late to stop the damage of Brexit being done.
"Increasingly, Scotland and the UK are on different political paths. We have to confront whether the better response to that is to have the ability to be independent and shape our own future."
Instead she said: "We also want to contribute Scotland's ideas and talents to Europe's shared challenges and to uphold and exemplify our shared values."
She spoke out after talks with EU chief Brexit negotiator Michel Barnier, where she again set out the Scottish Government position.
Speaking ahead of the trip, the First Minister said: "People living in Scotland have shown once again that they comprehensively reject Brexit and want to remain as a European nation.
"Membership of the EU not only has huge economic benefits for Scotland, but is the basis of the core values we share around democracy, equality, co-operation and human rights.
"My engagements in Brussels are an opportunity to outline the Scottish Government's support for those values and how they contribute to a better Scotland, Europe and wider world.
"On issues such as climate change and tackling inequality we can all work together to ensure the wellbeing of our citizens, as well as the wealth of member states."
The First Minister is also due to meet EU president Jean-Claude Juncker later on Tuesday.