Labour Party chairman Paul Mooney said it was a vital servicee.
He said: "Having this facility based locally is hugely beneficial to local families and provides an excellent service.
"Any uncertainty over its future is a blow to our community, and we hope the unit's future is secured in the long term as promptly as possible.
"We want the people of Inverclyde to know we will be standing shoulder to shoulder with them in campaigning to keep this service based locally."
Party secretary, Joseph McFadden, added: "We hope the whole of Inverclyde will be consulted with and listened to regarding the future of Inverclyde Royal.
"It is vital for helping stabilise and grow our population to have a fully functioning hospital for the area."