One person wrote: "Don't let them get you down. There are still some civilised people left in Scotland, honest."
Another Twitter user wrote: "Just know that for every person that insults or attacks you, there is someone out there who stands with you!"
One other supporter said: "I love you and support you all the way! I apologise for the idiots out there who just don't know how to keep their awful comment to themselves."
The author has also retweeted a number of photographs from fans all around the world, inviting her to visit their country.
Rowling revealed yesterday that she had been "invited to relocate to France, Ireland and Brazil!" and joked: "I've got to be honest, if I'm leaving Scotland, the climate is something I probably wouldn't want to replicate first!"
The author said she was overwhelmed by the amount of "love and support" she had received, and thanked those who had given her their backing, writing: "Looking at those beautiful pictures reminds me how big the world is and how many more decent people there are than not, so thank you xxx."
And she received praise for a withering put-down she dished out to the writer of some notably offensive messages.
She wrote: "The internet doesn't just offer opportunities for misogynistic abuse, you know. Penis enlargers can also be bought discreetly."
The Casual Vacancy author suffered a flood of criticism on Twitter last year after it emerged she had donated £1 million (NZ$2.8 million) to the campaign for a No vote in the Scottish independence referendum.
- AAP