The incident happened in Manchester city centre close to Piccadilly Station on Wednesday, August 16 at around 6.30pm.
One of the injured men remains in hospital with “life threatening injuries.”
Detective Chief Inspector, David Moores, of the Serious Crime Division of the Major Incident Team said: “This incident occurred at a place where there would have been a lot of footfall, due to it being school summer holidays and after work for most people.
“There were a lot of people out walking and shopping, and the canal bridge heading towards the Northern Quarter was busy. We are now appealing to anyone, who may have mobile phone footage, to come forward to assist with our enquiries.
“We are also looking for CCTV and dashcam footage that might be available of the area at the time of the incident.”
Eye witnesses on the scene in Manchester city centre on Wednesday evening reported seeing a cordon put in place and Crime Scene Investigators arrive on the site while later a man was seen being taken into a police van, apparently having been arrested.
Officers were also seen speaking to customers at the Piccadilly Basin car park about what they may have seen.
Residents said at the time that though they often saw police cars in the city centre it was rarely on this scale.
Three men were arrested in connection with the incident.
Two of them have been released without charge while the third, a 21-year-old man, has been released on bail pending further enquiries.
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The scene at Piccadilly Basin has reopened but police have said their will be an increased presence over the next few days while their investigation continues.
DCI Moores said: “This is an extremely serious incident and the Major Incident Team are continuing to work tirelessly to investigate.
“We have now opened a major incident public portal where anyone can submit information that can help us with this investigation.”
The portal can be accessed at mipp.police.uk while anyone with any information can also call police on 101.
Alternatively, witnesses can contact independent charity Crimestoppers anonymously on 0800 555 111.