Enda Kenny and Shane Ross are understood to have been at odds over Sinn Féin's neutrality bill
The Taoiseach says reports of a 90-minute row with the Transport Minister at Cabinet yesterday have been "greatly exaggerated".
It is claimed Minister Shane Ross and super junior minister Finian McGrath - both members of the Independent Alliance - sought a free vote on a Sinn Féin bill that would allow neutrality be enshrined in the constitution in a referendum.
The bill aims to amend the constitution and ensure Ireland is prevented from declaring war or participating in any armed conflict without the agreement of the Dáil.
Dáil agreement would also be required for the state to aid any foreign power in the preparation or conduct of an armed conflict.
The bill - which Fine Gael and Fianna Fáil have indicated they are not supporting - is reported to have led to tensions during a Cabinet meeting yesterday.
Speaking on the Pat Kenny Show earlier today, Kevin Doyle - Group Political Editor of Independent News and Media - explained: "There's varying versions of how heated it got, but a few things are certain - the Taoiseach was having none of Shane Ross yesterday.
"When the abortion bill came up a few weeks ago, Fine Gael sent out a statement acknowledging the right of the Independent Alliance to have a free vote on any issue that wasn't in the Programme for Government. This issue is not in the Programme for Government.
"So Shane Ross went in with a legitimate expectation that he could have a free vote on it, and the Taoiseach was not up for it. Charlie Flanagan also held a very firm line on it [...] And a whole raft of ministers had to intervene to kind of say 'can we not find a middle ground here and some sort of compromise?'
Enda Kenny, however, says he and Minister Ross had a 'constructive and straightforward' discussion on the issue at yesterday's Cabinet meeting - and that the reports had been 'greatly exaggerated'.
"I've made the point on many occasions that neutrality is a matter of fundamental Government policy," he stressed.