A recent internal costs review of the £97 million scheme has estimated the total amount needed to complete the development "could increase significantly".
The project, which is now on hold, is still in its planning stages and around three quarters of its funding is being allocated from the Government, with the remaining from Suffolk taxpayers.
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The outcome of the costs review is expected in September.
Council Leader Matthew Hicks said: "It's clear to me that whilst the significant project is being managed well, there is currently some uncertainty around the costs.
"If we're going to proceed and build these bridges, that uncertainty needs to be addressed right now.
"We're going to pause work temporarily, pending the outcome of this review. Then, based on sound and independent advice and considering everything we know about the project, Suffolk County Council will make a decision on the future of the Upper Orwell Crossings."
(LM)
