SDLP MLA Joe Byrne made the call following a statement from Minister Kennedy on the recent meeting of the North/South Ministerial Council.
Mr Byrne said he beliieved the two governments must now show real intent towards the A5 project by building the bridge.
He added: “It would be seen as a positive signal and would reassure the public at this time.”
Mr Byrne concluded: “The time has come for DRD and the Department of Transport in the Republic to start construction on the bridge. This is a project which is badly needed for economic development in the North West.”