Taoiseach Micheál Martin has said he believes that the dispute with Fianna Fáil TD for Cork East James O'Connor over the National Development Plan can be resolved.
Speaking in Slovenia this evening, he said that the National Development Plan is not an "exhaustive list of projects" and it was therefore possible for local authorities to bring forward plans for relief roads and by-passes.
Mr Martin said he plans to speak to his party colleague tomorrow again about the matter, and had been in touch with him already today and yesterday.
His comments come after Mr O'Connor said he is considering resigning from the party unless he gets a commitment from the Government on a roads project.
Should he resign, it would reduce the Government's numbers to 81, while the combined opposition numbers would then stand at 78.
The Dáil's youngest TD is angered by the failure to include a by-pass for Castlemartyr and Killeagh in the National Development Plan this week.
He voiced his concern on Cork local radio station C103 this morning.
RTÉ News understands that he has been in talks with the Taoiseach since Sunday night.
Mr O'Connor wants a firm, unambiguous commitment from the Government this evening that the road upgrade will proceed.
The €54m project was referenced by the Taoiseach and Public Expenditure Minister Michael McGrath at the launch of the NDP in Cork on Monday.
However, it was not included in the published document.
Mr Martin said he knew that Minister for Transport Eamon Ryan had "made it clear" he supports by-passes, something the Green Party leader had been saying "consistently".
He added: "We are all very conscious of the congestion in Castlemartyr and that Cork County Council are now doing an appraisal of that project."
Mr O'Connor, meanwhile, has said he will meet with the Taoiseach toorrow.
However, he reiterated that the Killeagh-Castlemartyr by-pass remains a red line issue for him.
Without a firm commitment to deliver it, the Cork East TD said he would have to resign from the party.
Additional reporting: Micheál Lehane