A police department in Galveston, Texas, has apologized after two white officers on horseback led a black man through the city’s streets on a rope.

Photographs shared on social media show Donald Neely, 43, flanked by two mounted police officers. Neely’s hands are bound behind his back, and one of the officers is holding an attached thick blue rope.

Following widespread criticism and outrage, Galveston police said it would end the practice.

The police department said in a statement: “We understand the negative perception of this action and believe it is most appropriate to cease the use of this technique.”

Neely’s sister-in-law, Christin Neely, was among those who criticized Galveston police. Neely had been “treated like an animal”, she said, adding that he was homeless and mentally ill, and the family often struggled to locate him.

She wrote on Facebook: “Now imagine scrolling FB and seeing said loved one being escorted to jail on foot by two officers on horses, hands cuffed behind his back with a rope attached. In 2019?”

Galveston’s police chief, Vernon Hale, confirmed the photos were genuine.

He said: “First and foremost I must apologize to Mr Neely for this unnecessary embarrassment. Although this is a trained technique and best practice in some scenarios, I believe our officers showed poor judgment in this instance and could have waited for a transport unit at the location of arrest.

Hale added: “We have immediately changed the policy to prevent the use of this technique and will review all mounted training and procedures for more appropriate methods.”

Police said Neely had been arrested under suspicion of criminal trespass, and was being led to a mounted patrol staging area. Hale said the officers were wearing body-cameras at the time of the incident, but did not say whether they would be disciplined.

Hale said the pair “did not have any malicious intent at the time of arrest”.

Civil rights groups said the image recalled the historical mistreatment of black people.

“This is 2019 and not 1819,” James Douglas, the president of Houston’s NAACP, told the Houston Chronicle.

“I am happy to know that Chief Vernon [Hale] issued an apology and indicated that the act showed poor judgment, but it also shows poor training. Even though the chief indicated that the technique would be discontinued he failed to address the lack of respect demonstrated by the officers in the episode.”

Leon Phillips, the president of the Galveston Coalition for Justice, said the pictures reminded him of racist images from the 1920s.

He told the New York Times: “All I know is that these are two white police officers on horseback with a black man walking him down the street with a rope tied to the handcuffs, and that doesn’t make sense. Period.”