The release of the Executive Council of Australian Jewry's report comes amid claims over the weekend that a local Jewish teenager was sent "heil Hitler" messages via social media, and asked on the phone whether her "family enjoyed being gassed".

ACT Police confirmed it is investigating the allegation.

The attack has prompted a local Jewish leader to demand police do more to combat anti-Semitism, which he fears is seeping into mainstream society.

The council's yearly report on anti-Semitism noted 13 attacks against the territory's Jewish community between October 2017 and September 2018, up from 10 in the previous year.

More than 360 anti-Semitic attacks were recorded across the country, up 59 per cent on 2016-17 cases. A third of incidents were attributed to neo-Nazi group the Antipodean Resistance.

The report's author, Julie Nathan, said a "noticeable emboldening of the far right across the Western world" was fuelling public acts of hatred, threats and violence towards the Jewish community.

More than half of the incidents reported in the ACT occurred during a series of abusive voicemail messages to a Canberra synagogue in May this year.

In other incidents referenced in the report, rocks were thrown through a synagogue's window and leaflets promoting white supremacy were distributed around the capital.

A local rabbi had been subjected to numerous attacks, including having his home vandalised and being verbally abused in front of his family, according to the report.

The incidents of anti-Semitism have sparked alarm in the territory's Jewish community, who are growing increasingly fearful of further attacks.

In an email to police, ACT Assembly members and federal politicians, obtained by The Canberra Times, Rabbi Shmueli Feldman said a local Jewish teenager had been targeted by an apparent Canberra-based neo-Nazi on the weekend.

"I have seen the messages where he proceeded to send the girl his extreme white supremacist views together with 'heil Hitler' messages," Rabbi Feldman's email said.

"Additionally, the girl involved says that this man called her on her phone and told her words to the affect of if her family enjoys being gassed. Needless to say the entire family are deeply traumatised by these events. I spent time last night providing counselling to the family and advised them to make a police report today."

In the email, Rabbi Feldman described a series of anti-Semitic attacks in the past year, which he said had either been ignored or not appropriately investigated by police. They included:

Rabbi Feldman's email also referenced an incident in which eggs were thrown at a Jewish community centre in May.

He said images of the offenders had been provided to ACT Policing after the attack, which immediately followed news of Chabad ACT's plans to establish Canberra's first Jewish school in the area.

Police are yet to catch the culprits, and last month released CCTV footage of four suspects, albeit with their faces pixelated.

Rabbi Feldman said in the email that he feared the situation would worsen and that living in Canberra would "no longer be sustainable for Jewish families" if police continued with a "somewhat indifferent approach" to investigating hate crimes.

Rabbi Feldman did not wish to elaborate on the contents of the email when contacted on Monday by The Canberra Times.

But he warned that anti-Semitism was creeping back from the "fringe of society" into the mainstream, pointing to the recent infiltration of the NSW National Party by members with alleged links to white supremacist organisations.

He urged the community to speak out against anti-Semitism, saying a broad indifference to race hate contributed to the rise of Nazism.

"The only way to win is through love," he said. "And that means everyone doing their little bit in the community."

Federal Labor MP Mike Kelly, the subject of an anti-Semitic attack on his Queanbeyan office in September, said he was "dismayed and disgusted".

"We as a community must unite in loud and clear rejection of these right wing extremists and all forms of racism," he said.

"I believe right wing extremists have been encouraged by political events around the world and by the politics of fear and division in our own country. We all have a responsibility to call out and shine a light on these vile elements in our community and to embrace and include our neighbours, no matter what their race, colour or creed."