Figures revealed by the charitable trust shown the funding gap is around £26m higher than previously thought.
The trust has put back its expected completion date by a year – to 2019.
Garden Bridge Trust chairman Lord Mervyn Davies said it was a "crucial time" for the project and said it "would be a tragedy if the government withdrew their support now".
He has asked Transport Secretary Chris Grayling to extend its £15m underwriting of the project for a year to September 2017, from the Government’s existing £60m funding pledge.
The money has been earmarked as insurance against costs which would be triggered should the project collapse, but only until the end of next month.
Recent hold-ups in land negotiations and planning matters has increased the project cost by £10m.
The Thomas Heatherwick and Arup-designed bridge with planting design by Dan Pearson has been beset by controversy and a determined campaign for it to be binned, amid questions about the location and the use of public funds during a time of austerity.
But Heatherwick, who rose to prominence for his London Olympics cauldron design, has urged the nation to "hold their nerve" over the bridge and not "suddenly have no confidence in ourselves" following Brexit vote political turmoil.
The National Audit Office is investigating if former Chancellor George Osborne’s decision to give £30m to the project through the DfT provides value for money for the public purse.
A further £30m was pledged from Transport for London (TfL) under former Mayor Boris Johnson.
However Lambeth Council suspended negotiations around the lease because of growing concerns about the £30m TfL had contributed to the Garden Bridge scheme.
Negotiations continued after it was agreed £20m of that funding must be paid back over 50 years.
The bridge is set to feature 270 trees, 2,000 shrubs, hedging plants and climbers, 22,000 perennials, ferns and grasses and 64,000 bulbs, Willerby Landscapes secured the contract to build the garden in May last year.
To reach its fundraising goal the trust needs to raise a further £55.9m. It has raised just over £69m of private funding from 2013 to June 2016 and by the same month had spent nearly £36m of public money developing the project.