Footage of the group being shoved and dragged away by officers while performing the sunset prayer, or Maghrib, outside Sydney Town Hall on Monday sparked widespread outrage.
NSW Police said a senior officer agreed to let the praying finish before moving the men on during the protest against Israeli President Isaac Herzog's visit.
Some worshippers were moved on before that message was able to be relayed in "a noisy, dynamic and fast moving situation", a police spokeswoman said.
The police watchdog on Friday revealed it had received a "significant number" of complaints and it was in the public interest to investigate any alleged misconduct.
But Mr Minns has repeatedly refused to apologise for the actions of police, providing steadfast backing of officers who forcibly dispersed the worshippers.
"I genuinely believe NSW Police, their leadership, their regular officers, would never, ever have disrupted a prayer service," the NSW premier said.
Mr Albanese on Saturday expressed his concern.
"I'm concerned that the great deal of hurt which the Muslim community are feeling about the disruption of prayers, I understand that and I think that is something that needs a full explanation," the prime minister told Nine's Inside Politics podcast.
"I know that that has caused a great deal of distress."
Hours after Mr Albanese's comments, he joined Mr Minns at the NSW Labor country conference in Orange.
The pair entered the event together to a standing ovation from supporters, shook hands and took a selfie with Lismore MP Janelle Saffin.
"(It was) a special moment for me walking down the middle of the aisle on Valentine's Day with the prime minister," Mr Minns joked.
During a 30-minute speech, the premier listed boosting the number of police recruits as one of the state government's achievements.
Mr Albanese referred, as he sometimes does, to Mr Minns as "my friend".
"We work very closely with the Minns Labor government," he said.
The leaders did not take questions from the media.
Several civil liberties groups, including Amnesty International, welcomed the watchdog's move to look into any police misconduct.
The investigation of "deeply concerning violent scenes" needed to be comprehensive, without delay and involve public hearings, the NSW Council for Civil Liberties said.
"Transparency and accountability for police actions are not anti-police; they are pro-democracy, and increase public trust and confidence in the institution," it said.
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