The UK government has pledged its continuous support for the Thomas Heatherwick-designed Garden Bridge, but has reduced its financial guarantee from £15 million to £9 million.

Transport secretary Chris Grayling has extended the offer to underwrite funding for the £185 million project proposed across London's River Thames. The new offer is valid for an unlimited time period, but is for £6 million less.

The original £15 million government guarantee had been due to expire next month. The Garden Bridge Trust – the non-profit organisation behind the project – had only asked for a year's extension.

The new £9 million figure reflects the believed amount required to cover cancellation liabilities.

Speaking on Grayling's behalf, transport minister Lord Ahmad said: "The government wishes the exciting and innovative Garden Bridge project every success and has provided public funding to help get it off the ground."

"We have extended our agreement to underwrite cancellation costs but capped at the current level of £9 million," he added.

"The taxpayer must not be exposed to any further risk and it is now for the trust to find private sector backers to invest in the delivery of this iconic project."

Until recently Heatherwick's design was expected to cost £175 million – with £60 million in government funding and the remainder raised by the Garden Bridge Trust through private donations.

But it emerged last week that delays had increased the cost of the project by £10 million, and that a number of investors had pulled out over the last year, leaving the trust with a much bigger shortfall than the previous estimate of £30 million.

An investigation by television programme BBC Newsnight found that the project is still £62 million short.

A spokesperson for the Garden Bridge Trust said they are confident they will cover the shortfall, and described the government's decision as a clear sign of its support.

"The government has made it clear it wishes to continue to support the 'exciting and innovative' Garden Bridge and has agreed to extend a large part of its underwriting agreement," they said.

"The Garden Bridge trustees have agreed to explore any further underwriting required and are currently working with new private sector sources to build on the current support."

Billed as a "beautiful new garden floating above the River Thames", the 367-metre-long Garden Bridge was originally conceived by British actress Joanna Lumley.

It is set to be constructed between Temple and the South Bank, and will feature full-size trees and planted sections along its deck, with a "super-strength" copper-nickel skin covering the structure's underside and legs.

But the scheme has been mired in controversy since it was first proposed.

It has been called into question over funding sources and the fairness of the procurement process that led to Heatherwick being appointed as designer, with critics including RIBA president Jane Duncan, local politicians – Vauxhall MP Kate Hoey and three councillors from the London Borough of Lambeth – and campaigners Michael Ball and Will Jennings.

Heatherwick continues to defend the project. Speaking on a Newsnight programme last week, he said: "It is ready to go, and it is important that our society doesn't show that we suddenly have no confidence in ourselves."

The bridge was due to open in 2018, but the trust has now moved this back to 2019.