The bridge is set to be constructed at Narrow Water near Warrenpoint, County Down, and once completed will link County Down with County Louth.
Councillor Patrick Clarke said: “Discussions and plans for the Narrow Water bridge have been on the agenda for many years, but it has never been so close to a reality as it is now.
“After receiving a major funding boost from the EU late last year, it is extremely worrying that the whole project could now be in jeopardy due to the reluctance of the Finance Minister to release the money he pledged.
“This cannot continue and I am calling on the Finance Minister to make the funding available immediately, before the EU funding is lost and we are back to square one.
“The Narrow Water Bridge project will bring a much needed tourism and economic boost the area. Linking County Down with County Louth, the project will encourage greater travel between the two and increase opportunities for trade.
“I hope all the funding will be in place in the near future, with construction on this much wanted project commencing this year.”