Footage emerged last week of the attack, in Victoria Park, Tower Hamlets, on 22 March. Two mounted officers were on duty as the dog repeatedly attacked one of the horses.
A Metropolitan Police spokesman said at the time that the horse, Urbane, needed stitches to the wounds he suffered.
In an update after the incident, a spokesman for the force said the seven-year-old gelding had sustained wounds to his front legs, chest and belly, and was recuperating in the Met stables outside central London.
“He is being seen daily by a vet, who is making sure he is as comfortable as possible,” the spokesman said. “It is believed he will make a full recovery.
“Urbane has been inundated with apples and treats from concerned and kind members of the public.”
The spokesman added that the officer riding Urbane was not physically injured, and is being supported by his mounted branch colleagues.
In a further update, the spokesman thanked all those who had expressed their concern and sent good wishes to Urbane and his rider.
“The officers and horses at Bow Mounted Branch are very touched by all the kind words and support shown,” he said.
The dog was taken into police kennels after the incident.
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