Eleven Australians were among 400 people taking part in the Global Sumud Flotilla to Gaza before being intercepted by Israeli forces at gunpoint in international waters on Tuesday.
Israel's ambassador to Australia Hillel Newman said the activists were "certainly safe", had access to consular officials and would be deported following due process.
"No one is in harm's way ... the dealing with them was very sensitive," he told reporters in Canberra on Thursday.
Israeli Prime Minister Benjamin Netanyahu and Foreign Minister Gideon Sa'ar condemned their colleague National Security Minister Itamar Ben-Gvir's actions as "not in line with Israel's values".
Dr Newman said despite the degradation of the activists "no one was hurt".
"A country is not measured by the actions of one politician, but how the government responds to actions which are disgraceful," he said.
A social media post by Mr Ben-Gvir overnight showed him gloating over flotilla participants as they are forced to their knees by guards.
In the video, Mr Ben-Gvir, who remains a minister, walks through a crowd of detainees kneeling with their heads on the floor as he smiles and berates a man whose hands are zip-tied.
It is unclear whether any of the Australians are in the video, but Jacinta McEwen - whose son Surya McEwen has taken part in the aid effort - said she was horrified.Â
"I'm absolutely outraged that Ben-Gvir is bragging about basically torturing the participants," she told AAP.
"I'm really worried (Surya) is going to be hurt."
Mr McEwen has previously been detained by Israeli forces after taking part in other flotilla attempts.
Last time, he had his head slammed against a steel wall and a dislocated shoulder, a broken collarbone and broken ribs from being kicked in the chest, his mother said.
A report from Adalah Lawyers - a legal team acting for Arab minority rights in Israel - said the latest group of flotilla participants had passed the initial processing stage of Israeli immigration and were being transferred to Ketziot Prison.
The lawyers have received complaints from the activists about the use of tasers and rubber bullets, sexual harassment and degradation.
But Bernadette Zaydan, a lawyer representing some of the Australians, has yet to receive clarity from Israeli or Australian authorities.
"The Israeli military is not forthcoming with information and they seem to do this to intentionally waste our resources," she told AAP.
The Australian cohort was expected to face a tribunal before being deported, though the lawyers were struggling to find out where they could end up, Ms Zaydan said.
Foreign Minister Penny Wong has called for the release of the Australians after condemning the video posted by Mr Ben-Gvir.
"The images we have seen posted by Israeli Minister Ben-Gvir - who Australia has sanctioned - are shocking and unacceptable," Senator Wong said on X.
"We condemn his actions and the degrading actions of Israeli authorities towards those detained."
Senator Wong directed the Department of Foreign Affairs to call in Dr Newman to reinforce her message.
He met with departmental officials in Canberra on Thursday.
The Executive Council of Australian Jewry slammed Mr Ben Gvir for his "disgraceful" treatment of the activists.
"Nothing can excuse the appalling behaviour displayed by minister Ben Gvir against a group of people who were being held in custody in Israel," president Daniel Aghion said.