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One of Georgia's most well-known transgender women has been killed in her home, a day after the country's parliament passed a major anti-LGBT bill.

Local officials say Kesaria Abramidze, 37, was stabbed to death in her flat in the capital, Tbilisi, on Wednesday.

The interior ministry said it was investigating a "premeditated murder committed with particular cruelty and aggravating circumstances on gender grounds".

A 26-year-old man has been arrested in the case that has shocked the small South Caucasian nation. Georgian media reported he was known to the victim.

Rights groups have linked the killing to the new anti-LGBT law, arguing the government's promotion of it had fuelled transphobic hate crime.

Georgian President Salome Zurabishvili, who opposed the new law, said the "horrendous murder" raised urgent questions about hate crimes and discrimination.

The legislation from Prime Minister Irakli Kobakhidze's government severely restricts rights for LGBT people.

It introduces a ban on same-sex marriage, gender-affirming surgeries, child adoption by non-heterosexuals and the promotion of same-sex relationships in schools.

The bill sailed through parliament on Tuesday in an 84-0 vote, despite criticism from rights groups.

The ruling party said the "Protection of Family Values and Minors" bill was designed to protect a majority of Georgians seeking protection from "LGBT propaganda".

But local LGBT rights campaigners said the government had used homophobic and transphobic language and ideas in promoting the bill.

Several activists directly linked what they said was the government's harmful rhetoric to the killing of Ms Abramidze.

One of the first openly trans public figures in the country, she had represented Georgia in international trans pageants and had more than 500,000 followers on social media.

"Political homophobia, biphobia, and transphobia have become central to the government’s official discourse and ideology," said local human rights group the Social Justice Center.

"Kesaria Abramidze's killing cannot be viewed separately from this overall grave context," it added.

Progressive politicians outside the country have also linked the killing to the government's legislative agenda.

"Those who sow hatred will reap violence. Kesaria Abramidze was killed just one day after the Georgian parliament passed the anti-LGBTI law,” wrote German lawmaker Michael Roth, the social democratic chair of the country's foreign affairs committee.

European Union figures had already condemned the legislation when it passed earlier this week, saying it further jeopardised the country's stated aim of joining the EU.

Josep Borrell, the EU's foreign policy chief, said the law was "further derailing the country from its EU path". He called on the Georgian government to withdraw the law.

The legislation undermines the "fundamental rights of the people" and increases discrimination and stigmatisation, he added.

The British embassy has also expressed "serious concerns".

Rights groups have characterised the Georgian legislation as being similar to Russian laws which severely restrict LGBT rights.

The Washington-based think tank Freedom House said the bill was "pulled directly from the Kremlin's authoritarian playbook".