Fresh wreaths of flowers have been laid at Bondi beach, children have cooked meals for those in need and Anthony Albanese has welcomed the opportunity to “wrap our arms around” the Jewish community as Australia holds a national day of mourning for the victims of last month’s terror attack.

Under the banner of the New South Wales government’s One Mitzvah for Bondi initiative, all Australians were urged to do a good deed – or mitzvah – on Thursday to mark the day of mourning.

The prime minister said the day was about remembering the 15 victims of the 14 December attack, which he called a “stain on our nation”.

“It’s an opportunity for us as a nation to wrap our arms around the Jewish community because people were targeted because they were Jewish Australians. Every Jewish Australian felt that very deeply that evening, and ever since as well,” he said on Thursday.

“Today, we share their grief. A grief with no ending, only a beginning.”

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In Paddington in Sydney’s east, children came together to cook meals for the needy. On the menu at Kids Giving Back on Thursday morning was Thai red curry and a salad with parmesan and pepitas. The 350 meals will be distributed to vulnerable communities in Macquarie Park.

The co-founder and CEO, Carole Schlessinger, started the non-denominational charity 13 years ago, basing it on the Hebrew concept of tikkun olam, or repairing the world.

“It’s giving people hope and agency when everything feels so dark,” she said. The kitchen was a place to focus on positivity and the “basic kindness people need to overcome the evil that’s in the world”, she said.

Carole Schlessinger (middle), CEO of Kids Giving Back, help some of the families as part of the One Mitzvah for Bondi event. Photograph: Rémi Chauvin/The Guardian

Bondi’s Chabad community chose the theme “light will win” for the day of mourning.

Mother-of-three Rachel Filler, from Vaucluse, carried her 10-month-old, Marlee, as she chopped carrots with her elder daughters Lilah, six, and Emme Biondi, eight.

“I’ve told the children we’re doing a mitzvah to give back in a world that can sometimes be not kind. It’s never a bad lesson to learn,” she said.

“I know a lot of people in the Jewish community who are afraid to go outside after everything that happened. But it’s nice to be able to show kids that the world is still good, there are still good people and this is proof of it.”

Nearby, brothers Noah, seven, and Jordan Shabad, five, peeled potatoes.

“A mitzvah is to help people,” said Noah. “We’re cooking for other people, that will make them happy.”

After tidying away, and while 12 hot plates bubbled with curry, the children decorated the lids of the cardboard containers that would carry the meals.

Among rainbow, love heart and sunshine motifs, one message simply read: “I hope this meal brightens your day.”

Children write messages of support to those who will receive the meals cooked by them. Photograph: Rémi Chauvin/The Guardian

The state government said about 2,500 acts of kindness had been registered with One Mitzvah for Bondi’s website, with many more taking place without being counted.

“My canoe club is now running a Harmony Paddle. We will paddle gently down the River, pausing to reflect and light candles on bamboo containers, letting them float into the evening”, one person wrote in their submission.

Another said they had gone food shopping for a 90-year-old neighbour, while another had collected rubbish from the beach.

“We have been staggered by the support and uptake of people going out their way to do ‘one mitzvah’, not just in NSW but across Australia. Small acts of kindness that together have become an overwhelming wave of support, and we know how much it has meant to both Jewish community and the Bondi area as a whole”, the NSW minister for multiculturalism, Steve Kamper, said.

At Bondi Pavilion, metres from the scene of the attack, fresh wreaths of flowers were laid near piles of memorial stones, inspired by a Jewish tradition to lay a stone at a grave.

A man stands by the piles of memorial stones in memory of the 15 victims of the Bondi beach shooting on 14 December. Photograph: Steven Markham/AFP/Getty Images

A chaplain watching on said people had been coming and going all day from the memorial, some to lay stones, others to simply watch on and pay their respects.

Vibeke and Jan, who are from Denmark and are on holiday in Sydney, visited the memorial to lay a stone while touring through Bondi.

“The whole world knows about what happened,” Jan said.

Mourners will also gather inside the Sydney Opera House on Thursday evening for the official national memorial service, organised by the Chabad of Bondi, with support from the federal government, community partners and faith leaders.

In Melbourne, hundreds of mourners gathered at Paul’s Anglican cathedral for a sombre service to commemorate the 15 people killed in the Bondi attack.

The state governor, Margaret Gardner, and the premier, Jacinta Allan, joined attendees for the morning vigil.

The Anglican archbishop of Melbourne, Dr Ric Thorpe, said political and community leaders had come together to mourn the lives of the 15 people “cut tragically short on Bondi beach”.

“We stand side by side with members of the Jewish community here in and Melbourne and throughout Australia, and with countless people the world over who, like us, condemn antisemtiism, hate crime persecution and violence,” the Anglican Dean of Melbourne, Dr Andreas Loewe, said.

At the end of the vigil, the name of each victim was read aloud by reverends before a minute of silence.

Across Victoria, flags were being flown at half mast at all government buildings and landmark buildings will be lit up in white as a symbol of light tonight.