The SNP leader will also launch a "Made in Scotland" festival of theatre, dance and music performances in Belgium. She she said she hoped Scotland's separate stance on Brexit was being "acknowledged and welcomed" in Europe.
That contrasted with results south of the border, where Nigel Farage's Brexit Party took most seats.
Ms Sturgeon said: "People living in Scotland have shown once again that they comprehensively reject Brexit and want to remain as a European nation".
She told how Scotland and the rest of the United Kingdom are "increasingly" on different political paths.
And addressing the European Policy Centre think tank in Brussels, she said: 'The basic values of the EU are ones we identify with. "We like the idea of independent nation states co-operating for the common good".
She said her government deeply regretted the UK's vote to leave the European Union and added: "We think the best option - for the United Kingdom, as well as for Scotland - would be to remain in the EU". For all the current challenges we face, my hope - and my belief - is that it will grow further in the years and decades ahead'.
Ms Sturgeon stated: "We want not simply to benefit from free movement and free trade - although we do".
Meeting European Commission president Jean-Claude Junker and EU Brexit negotiator Michel Barnier while in Brussels, she also criticised the United Kingdom government, describing its Brexit position as filling her with "despair" as there was no "coherent or credible United Kingdom government position to speak of".
The Brexit process has however been stalled by Theresa May's failure to get her Withdrawal Agreement through Parliament, and by her subsequent departure as Prime Minister - with Conservatives now focused on the contest for her successor.
A United Kingdom government spokesperson said while diplomatic staff regularly provide support to devolved administrations, "a balance must be struck to avoid supporting activities meant to campaign for policies contrary to HMG's position".