Assistant Foreign Minister Matt Thistlethwaite has also declared the ALP won't tolerate anti-Semitism in its own ranks and that any such behaviour will be dealt with swiftly and harshly.
Asked if she would apologise to the Jewish community, Senator Wong said she was "desperately sorry for what has occurred in our country and what the Jewish community have experienced".
"Sorrow isn't political; sorrow is felt when we go to our places of worship, when we light a candle for those lost and for those grieving, when we hold our children close," she told her hometown newspaper The Advertiser in Adelaide.
"These are moments where I think all of us have grieved."
She would visit Bondi "when it's appropriate" and had not attended any victims' funerals because "funerals are intensely personal, and generally family-led".
"I respect what families want and I respect their grief, which is overwhelming," she said.
Mr Thistlethwaite, who is also assistant minister for immigration, said he had visited Bondi "countless times" since the attack, including the "very moving" vigil.
"My message to the Jewish community is that our government is here to support you, to help you," he said on Saturday.
"We are acting on the recommendations of the Jillian Segal report to toughen laws, to ensure that we combat anti-Semitism in Australia.
"We owe it to Australia's Jewish community to act now, to keep them safe and to put in place measures to ensure they are free to practise their religion and their faith in Australia in safety."
Referencing an internal letter sent to ALP leaders in NSW calling for stronger action to fight anti-Semitism within the party's ranks, the minister said Labor "would not tolerate" such behaviour.
"I would encourage any member who witnesses or sees any form of anti-Semitism within our party to report that and ensure that it's investigated as soon as possible," he said.
Ten people remain in Sydney hospitals recovering from injuries sustained in the December 14 attack at Bondi.
Four remain in a critical condition, while the other six are stable, NSW Health said on Saturday.
The firebombing of a rabbi's car in Melbourne on Christmas Day was an "unspeakable attack" and Senator Wong said she condemned it, "particularly when the Australian Jewish community is mourning after the horrific events of Bondi".
Melbourne police continue to search for a person of interest over the attack on a car bearing a Hanukkah sign.
On Friday, they released a picture of 47-year-old John Argento, who also goes by John Seckold.
Anti-Semitism was "unacceptable and … the government has acted", Senator Wong said.
"Of course, always in politics and in life you always regret what more could have been done. I think we've made that clear. We acted but we have to do more and we are."
Asked if Australia should tighten immigration, Senator Wong said Home Affairs Minister Tony Burke had announced the strengthening of visa cancellation and visa refusal powers.
"I think that's the right thing to do," she said.
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