Flanked by Attorney-General Michelle Rowland and Home Affairs Minister Tony Burke, Mr Albanese outlined a package of new laws set to be introduced to parliament early next year to tackle hate speech and beef up laws to cancel visas of non-citizens who preach hate.
The laws were first flagged last week, but the government will also introduce a new aggravated offence targeting adults who seek to influence and radicalise children.
The announcement is unlikely to mollify members of the Jewish community who have been calling for the prime minister to announce a national royal commission into the Islamic State-inspired mass shooting, which claimed 15 innocent lives eight days ago.
Mr Albanese's approval rating has plunged since the Bondi massacre, although Opposition Leader Sussan Ley's standing has also fallen after her pointed criticism of the government, according to a Resolve survey published on Monday.
Mr Albanese apologised to the Jewish community after he was booed multiple times as he attended a Bondi Beach vigil for the victims of the attack on Sunday evening.
"Emotions were raw, and a lot of people in the community are hurting and angry, and some of that anger was directed towards me," he said on Monday.
"I understand that as prime minister, I feel the weight of responsibility for an atrocity that happened whilst I'm prime minister, and I'm sorry for what the Jewish community, and our nation as a whole, has experienced."
The same crowd applauded David Ossip, president of the NSW Jewish Board of Deputies, when he called for a royal commission.
The federal government had previously backed a NSW-led royal commission and launched a more limited review of its own, led by former intelligence chief Dennis Richardson, into federal intelligence and law enforcement agencies.
Foreign Minister Penny Wong earlier on Monday said the government's focus was on keeping Australians safe and the intelligence review would provide assurance faster than a broader royal commission.
Earlier on Monday, the opposition's most senior Jewish MP, coalition education spokesman Julian Leeser, delivered a scathing condemnation of Mr Albanese for not calling a royal commission into the terrorist attack.
"The Jewish community of this country cannot survive on the crumbs of this government and this appalling prime minister who is always late to the party and who wants the Jewish community of this country to live in his half measures," he said on Monday, slamming the lectern with his palm as he spoke.
Labor backbenchers Mike Freelander and Ed Husic have reportedly broken ranks to call for a federal royal commission.
In a move to ramp up pressure on the government, the coalition on Monday released its own terms of reference for a royal commission.
The opposition's proposed inquiry would deliver an interim report by June 2026 and look at how commonwealth and state governments, as well as the media, education and cultural sectors, have allowed anti-Semitism to fester and contributed to the terrorist attack.
Mr Albanese rubbished the coalition's claim that a royal commission could report back within the space of six months, when they typically take a number of years.
"The idea that we would have multiple royal commissions, as well as a review, running at the same time is going to simply delay action," he said.
NSW Premier Chris Minns earlier on Monday said the NSW royal commission would be able to inquire into the roles of federal law enforcement agencies ASIO and the AFP.
