It is understood that so tense was the disagreement that Mr Ross threatened to “pull the plug” on the Government, which is just four weeks old.

Ten days ago, Mr Kenny approached Mr Ross, informing him of his desire to nominate someone to become vice-president of the European Investment Bank (EIB) without undergoing a formal vetting process. The names of former taoiseach John Bruton and former Department of Finance secretary general John Moran have been linked to the prestigious post.

Mr Ross adamantly refused to sanction the move and Mr Kenny has been forced to abandon his plan.

Mr Ross insisted that all appointments of this nature must be subject to a rigorous selection process and that he would not approve Mr Kenny’s proposal.

It is understood that Mr Ross repeatedly asked Mr Kenny for the name of the person he wished to promote, but the Taoiseach repeatedly refused to answer.

Following the row, Mr Ross was said to be “absolutely furious”.

Shane Ross

“He was fit to kill Kenny. He was bulling, absolutely furious. He threatened that if he went ahead with this crony appointment, then he would pull the plug on the whole thing,” said one source.

Several Fine Gael ministers have confirmed the matter never came before Cabinet, nor was it discussed in the pre-Cabinet meeting of the party’s ministers.

The sides have since been locked in arguments over how to resolve the matter, but it appears that Mr Ross has got his way and that a selection process similar to the one to choose the last Central Bank governor will be utilised.

Three days ago, the Department of Finance posted a notice on its website seeking applications for the post, which commences in August for a four-year term.

A spokesman for Mr Kenny confirmed that the matter has been the subject of engagement between the two men, and that a process is under way. He rejected claims that there had been a disagreement between Mr Kenny and Mr Ross, or that a row had taken place.

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This version of events, however, has been dismissed by several senior sources.

Mr Bruton told the Irish Examiner he was not in a position to confirm the details of the story.

Mr Moran told this newspaper he was “flattered” at the suggestion but he said taking the post would preclude him from doing many things he is currently enjoying doing.

“It would cut me off from all the other stuff I love doing, so no, it’s not for me,” said Mr Moran, who is already a board member of the EIB.

Along with all other EU governments, Ireland is a member of the EIB, which is the EU’s investment bank, located in Luxembourg.

The permanent executive body of the bank is the EIB management committee, which consists of the bank president and eight vice-presidents.

According to the advert, the person appointed as vice-president will be a “significant additional resource” for Ireland at EU level and a source of informal influence on Ireland’s behalf at the EIB.

News of this row comes amid tensions between Fine Gael ministers and their Independent counterparts.

Monday’s Irish Examiner revealed how a series of incidents in the first three weeks of Government soured the mood between ministers.

Super junior minister Finian McGrath spoke of Government “not being an easy place for me to be”.