Hundreds of protesters gathered outside Rochdale Police Station after footage of an officer kicking and stamping on a man's head was shared widely on social media.
Greater Manchester Police (GMP) said it understands the "immense feeling of concern and worry that people feel" after the footage from Manchester Airport emerged.
The force added the demonstration on Wednesday night ended "without incident".
Sky News understands the people seen being arrested in the video come from the Rochdale area and a large crowd came together just after 10pm to show solidarity for the men.
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Tap hereAssistant Chief Constable (ACC) Wasim Chaudhry of Greater Manchester Police said an officer "has been removed from operational duties" in relation to the footage.
it is understood the officer has not been suspended.
The video, said to have been filmed at Terminal 2 of the airport on Tuesday evening, shows an officer with a Taser in his hand appearing to kick and then stamp on the head of a man who is lying face down on the floor, with a woman kneeling beside him.
A second man was also struck by the officer.
On Thursday morning, ACC Chaudhry added: "A protest held last night outside Rochdale Police Station about our response at Manchester Airport has concluded safely, without incident.
"We understand the immense feeling of concern and worry that people feel about our response and fully respect their right to demonstrate their views peacefully.
"We have already referred our actions to the Independent Office for Police Conduct (IOPC) and will be in further discussions with them today.
"We have spent the evening listening to community feedback and will continue to engage with communities and elected members to maintain strong partnership links and understand local views."
ACC Chaudhry earlier described the video as "truly shocking" and said it shows images that "people are rightly extremely concerned about".
He went on to say that three officers had been assaulted when the force responded to an incident at the airport.
ACC Chaudhry continued: "One female officer suffered a broken nose and the other officers were forced to the ground and suffered injuries which required hospital treatment."
GMP also acknowledged concerns about "conduct within the video" but said officers had arrived at the scene with guns and there was a "clear risk" of "their firearms being taken from them".
A force spokesman said: "Whilst attempting to arrest one of the suspects of the earlier altercation, three officers were subject to a violent assault, where they were punched to the ground.
"A female officer suffered a broken nose and all three were taken to hospital for treatment.
"As the attending officers were firearms officers, there was a clear risk during this assault of their firearms being taken from them.
"Four men were arrested at the scene for affray and assault on emergency service workers.
"We acknowledge the concerns of the conduct within the video and our Professional Standards Directorate are assessing this."
Home Office minister Dame Diana Johnson posted on X, formerly Twitter: "I am aware of disturbing footage from an incident at Manchester Airport this afternoon and understand the public concern it has prompted.
"I have asked for a full update from Greater Manchester Police."
Mayor of Greater Manchester Andy Burnham said he had raised concerns about the airport incident with the deputy chief constable.
He said: "I have seen the disturbing video footage circulating of a GMP officer at Manchester Airport and recognise the widespread and deep concern this has caused in Greater Manchester and beyond.
"The deputy mayor and I have raised these concerns with the deputy chief constable."
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