It is being built to follow the course of the Knock, Connswater and Loop rivers and is backed by two Stormont Departments and Belfast City Council.
The Connswater scheme is also aimed at alleviating flooding as well as developing a public space for cyclists and walkers.
The contract to build riverside walkways, flood defences and cycle paths was awarded to two firms - SIAC NI Limited and Galliford Try Infrastructure and is being funded by Belfast City Council, the Big Lottery Fund, the Department of Agriculture and the Department for Social Development.
But, BBC NI has alleged today that a dispute has broken out between the contractors and Belfast City Council.
Work surrounding the creation of new flood defences has run into difficulties and Belfast City Council and the two firms are trying to resolve the dispute.
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Commenting, the local Alliance representatives Cllr Máire Hendron and Chris Lyttle MLA have said it is crucial that there is agreement as regards the Connswater Community Greenway project to ensure that the scheme can be completed as soon as possible.
Cllr Máire Hendron said: "This is a very exciting scheme and it is crucial that it is delivered on time. This project offers massive leisure potential and potential in terms of increasing sustainability through the provision of cycle paths.
"It's vital that there is agreement to allow quick progress on the project," she said.
Chris Lyttle MLA said: "This is a very important community scheme, a lot excellent work has already been done by all those involved and I hope that it proceeds as quickly as possible.
"This is a very positive project for east Belfast and we must make the most of the natural resources we have in the area.
"This scheme could also help boost the economy in the area and is a key component of the east Belfast of the future," he said.
Work originally started last November on the planned new bridges, riverside walkways and cycleways.
The Stormont First Minister Peter Robinson welcomed the announcement that SIAC (NI) Ltd and Galliford Try Infrastructure had been awarded the contract to develop the imaginative 'green' project, having supported and encouraged the scheme from its first inception.
The DUP First Minister and East Belfast MLA said that the project represented a significant investment in the local economy.
"I welcome this milestone in the development of the Connswater Community Greenway and East Belfast Flood Alleviation project.
"This major regeneration scheme represents a significant financial investment of some £32m and I congratulate the East Belfast Partnership for their initiative in bringing this innovative project forward," he said, at the time.
See: Welcome For Connswater Parkway Project
(BMcC/GK)
