https://www.bbc.co.uk/news/uk-england-manchester-54960088The wall is being demolished as part of £10m redevelopment plans.
Mr Karney said it was "a mistake" that the wall, designed by Japanese architect Tadao Ando, was built in 2002.
He said: "Our pledge to the public is that we are going to get it right this time. We want what everyone in Manchester wants, to look on the gardens with affection and pride."
Some of the structure, which is attached to a privately-owned building, will remain for now and proposals for the area, which include extended gardens and improved lighting, will be published in two weeks.
Work to demolish the free standing wall is expected to be completed this week.