The leader of the Conservative group at City Hall says he has "yet to be persuaded" about the merits of the proposed Garden Bridge between the South Bank and Temple.
Andrew Boff, who is seeking selection as the Conservative candidate for Mayor of London, made the comments at hustings on Wednesday night organised by the Centre for London think tank.
Answering a question about the Garden Bridge from the audience, Andrew Boff said: "The case hasn't been made.
"I don't want to spend £60 million of taxpayers' money on something that doesn't seem to have made the case.
"Not only that, I don't actually think it's going to the right places. If we'd had a Garden Bridge ... going from perhaps Beckton over to Bexley or Greenwich, that would have been a much better solution.
"But where it is, I've yet to be persuaded."
The other candidates didn't address the question directly until they were pressed for their views by chairman David Willetts.
Stephen Greenhalgh, currently deputy mayor for policing & crime, said he would review the project if elected next year: "I'm not a passionate person for the Garden Bridge, but it's small beer. In the grand scheme of things it's a small decision whether you [cancel] that or not, frankly."
Zac Goldsmith MP was the only candidate to express enthusiasm for the Garden Bridge. "I'm drawn to the design," he said. "I think it's a beautiful design.
"I think it's the kind of thing that in a few years' time people will look back and think this is one of those things that makes London more interesting, more dynamic, more beautiful.
"It's not a project that I'd like to pull the plug on.
"I accept that it's costly, but in the context of the TfL budget, in the context of the vast amounts of TfL waste, I think this is a project we can justify.
"I don't think London will regret this bridge after it has happened."
The fourth candidate, Syed Kamall MEP, seemed to be confused between the Garden Bridge and the proposed Nine Elms bridge, answering the question with comments about the Westminster Boating Base in Pimlico.
Garden Bridge Trust executive director Bee Emmott said this week: "London is a living city, always improving and evolving and the Garden Bridge will continue that tradition. It will be a showcase for innovation, displaying the best of British design and landscaping talent and adding to the capital's rich and diverse heritage.
"It will be wonderful addition to the River Thames, providing a beautiful new garden floating above one of the world's great rivers. It is both innovative and practical, serving as a free bridge for Londoners to use and enjoy every day, getting them to their destinations via a new and healthy route."
In July the Garden Bridge Trust published the results of a ComRes opinion poll which claims 77 per cent of Lambeth and Westminster residents support the new bridge.
• On Tuesday 15 September Lambeth's planning applications committee is expected to approve detailed plans for the net loss of 25 trees on the South Bank as part of the Garden Bridge project.