One of two white police officers who rode through the streets of Galveston, Texas, on horseback escorting a black male suspect walking tethered to a rope is heard saying: "It looks so bad", according to a newly released police video footage of the incident.

The spectacle was caught on the officers' body cameras during their August 3 trespassing arrest of Donald Neely, who family lawyers have said is known to city police as someone who suffers from mental illness and regularly sleeps on the streets.

A still photo of the arrest captured by an onlooker and posted on social media went viral, prompting a public outcry.

The bodycam videos, publicly released on Wednesday, shed new light on the two officers' encounter with Neely as they took him into custody using a procedure that mounted police in their department were trained to employ when no transport vehicle was available.

At one point, officer Amanda Smith, seen leading Neely on a blue nylon rope she has fastened to his handcuffs, cautions him to "stop" at an intersection and to "stay next to me, because I'm gonna drag you if not."

Her patrol partner, Patrick Brosch, at least twice voices discomfort at the appearance of what they are doing, saying at the outset: "This is going to look really bad."

When Brosch reiterates how the scene will "look so bad," Neely is heard responding, "I'm not embarrassed," to which Brosch replies: "I'm glad you're not embarrassed, Mr. Neely."

Neely, forced to trudge several blocks between the horses with his hands cuffed behind him, was eventually handed over to another officer with a patrol car at an outdoor staging area.

Brosch and Smith have been placed on "modified duty" pending Galveston Police Chief Vernon Hale's review of a report on the incident submitted by the county sheriff earlier this week, said city spokeswoman Marissa Barnett on Thursday.

A separate Texas Department of Public Safety review determined no criminal investigation of the officers was warranted. But Hale will decide whether any disciplinary or other actions should be taken, Barnett said.

The Galveston Police Department said it no longer uses rope for arrests.