Prime Minister Anthony Albanese has announced a suite of legislative and other action to combat antisemitism including new measures against hate speech and extra power to reject visas.

The package, unveiled after a meeting of cabinet’s national security committee on Thursday morning, comes after days of anger in the Jewish community, where many people feel the government has not done enough against antisemitism since the October 2023 attack on Israel by Hamas.

The legislative measures include:

• an offence of aggravated hate speech for preachers and leaders who promote violence

• increased penalties for hate speech promoting violence

• making hate an aggravating factor in sentencing crimes for online threats and harassment

• developing a regime for listing organisations whose leaders engage in hate speech, promoting violence, or racial hatred

• developing a narrow federal offence for serious vilification based on race and/or advocating racial supremacy.

The Home Affairs Minister, Tony Burke, will be given stronger powers to cancel or reject visas for people who “spread hate and division” in Australia or who would do so if they were allowed to come to this country.

Albanese also said leading business figure David Gonski would lead a year-long taskforce “to ensure the Australian education system prevents, tackles and properly responds to antisemitism”. Gonski led the seminal schools inquiry that reported to the Gillard government.

Those also on the Gonski taskforce will include the government envoy to combat antisemitism, Jillian Segal.

Also, the eSafety commissioner Julie Inman Grant, Segal and the communications department are to provide online safety advice on addressing antisemitism.

Albanese said the government would fully adopt the Segal report on ways to combat antisemitism. Some of the measures in the report, presented months ago, have been implemented but the more controversial recommendations have not.

Albanese’s news conference was also attended by Burke, the Commissioner of the Australian Federal Police, Krissy Barrett, Education Minister Jason Clare and Segal.

Albanese said the government had already implemented recommendations from the Segal report on combating antisemitism and “we’ll continue to work through the implementation of the 13 recommendations in consultation with the Jewish community and the envoy”.

Asked whether he regretted not acting earlier with more strength and conviction on antisemitism, and whether he would apologise to the Jewish community, Albanese said “My heart goes out to Jewish Australians. Is there more that can be done? There is always more that can be done. Always. And quite clearly, there’s more to do.”

Asked whether a statement of contrition from him or the broader community would help healing, he said, “I, of course, acknowledge that more could have been done, and I accept my responsibility for the part in that as prime minister of Australia.

"But what I also do is accept my responsibility to lead the nation and unite the nation. Because what people are looking for at this time isn’t more division. They are looking to come together,” he said.

He said he had “done my best to respond. Do I regret anything? Anyone in this position would regret not doing more, and any inadequacies which are there. But what we need to do is to move forward. We are taking action. We have taken action.”

Albanese rejected suggestions that he had not engaged face-to-face this week with the Jews at Bondi, saying he had been to homes in Bondi and met with families who were grieving, as well as meeting with the community leaders at an interfaith memorial service at St Mary’s Cathedral on Tuesday.

The funeral of 10-year-old victim Matilda was held on Thursday morning.