JK Rowling’s comments about new hate crime laws “are not assessed to be criminal”, police have said, as they confirmed no further action would be taken.

The Harry Potter author dared police to arrest her on social media over the legislation that came into force in Scotland this week.

The new measures aim to tackle the harm caused by hatred and prejudice, extending protections from abusive behaviour to people on grounds including age, disability, religion, sexual orientation and transgender identity.

What are Scotland’s new hate crime laws?

Those who support the new laws insist they will make Scotland more tolerant. But critics such as Rowling claim the legislation could stifle free speech – and fails to extend these protections to women.

The Scottish government has said separate laws will be brought in specifically to tackle misogyny.

The writer, who has lived in Scotland since 1993, has become an outspoken critic of the Scottish government’s stance on trans rights, including its recent gender recognition bill which was blocked by Westminster.

In response to the police’s decision on Tuesday, Rowling tweeted: “I hope every woman in Scotland who wishes to speak up for the reality and importance of biological sex will be reassured by this announcement, and I trust that all women – irrespective of profile or financial means – will be treated equally under the law.”

Posting previously about the issue on social media, Rowling, who was out of the country at the time, added if what she had written was an offence under the Hate Crime and Public Order (Scotland) Act – which came into force on Monday – she would “look forward to being arrested when I return to the birthplace of the Scottish Enlightenment”.

In the post complained about, Rowling lashed out against transgender women, including double rapist Isla Bryson, who was jailed for eight years last year.

The post was in reaction to comments from Siobhan Brown MSP, a Holyrood minister, who said people “could be investigated” for misgendering someone online.

This evening, the community safety minister told Sky News’ Trevor Phillips on the Politics Hub that the bill had a “very, very high threshold” for criminality.

Rowling claimed that the new legislation was “wide open to abuse by activists who wish to silence those of us speaking out about the dangers of eliminating women’s and girls’ single-sex spaces”.

The 58-year-old claimed: “It is impossible to accurately describe or tackle the reality of violence and sexual violence committed against women and girls, or address the current assault on women’s and girls’ rights, unless we are allowed to call a man a man.”

First Minister Humza Yousaf has defended the legislation, saying there has been a “rising tide of hatred against people because of their protected characteristics” in recent years.

“I’m very proud of the hate crime act,” he said, adding it will “protect people from hatred, while at the same time protecting people in terms protecting people in terms of their freedom of expression”.

Equivalent ‘stirring up’ offences within the new act have existed for racial hatred since the 1980s and will be “policed sensibly”, he said.