The finance minister said he believed there was "a political smell" about the application to build a bridge at Narrow Water between counties Down and Louth, on 4 December 2012.
Sammy Wilson questioned the speed with which Environment Minister Alex Attwood had granted Article 31 planning permission to the bridge proposal.
He called for an investigation into the planning process.
Mr Attwood rejected the minister's comments in an intervention, but was asked to sit down by Deputy Speaker Roy Beggs who explained that only one minister was permitted to speak in a debate.
Earlier, the SDLP's Karen McKevitt had described the proposed bridge as "a genuinely symbolic cross-border project".
Ms McKevitt was proposing her party's motion calling for the Finance Minister to ensure that the remaining investment required for the bridge was committed "immediately".
She emphasised the tourism possibilities of the bridge, saying it would allow the Mournes, the Ring of Gullion and the Cooley peninsula to develop into a tourist region like the Ring of Kerry or the Causeway Coast.
The South Down MLA observed that people flying into Dublin Airport would be about 60 miles from "our shiny new bridge".
William Irwin of the DUP said there were many other projects more deserving than the bridge.
He said the project "requires greater thought".
Sinn Fein's Chris Hazzard said the bridge proposal had "caught the imagination of the people of south Down and north Louth alike".
Ulster Unionist John McCallister said he had some concerns about the proposal, but added that he would support the motion provided it was not built at the expense of the Newry southern relief road.
Trevor Lunn of Alliance said the Narrow Water bridge was "a terrific scheme" and he backed the motion.
Replying to the debate, Mr Wilson said it would not be right for him to make a decision on the bridge project before his officials had reported back on its feasibility, and he argued that the SDLP motion should not have been brought to the house.
The motion was carried by 47 votes to 38.