Former Labour minister of state Senator Aodhán Ó Riordáin has said he finds the situation regarding the Taoiseach's future "unbelievable''.
He told the Seanad the discussion surrounding when Enda Kenny would stand down was taking place in the teeth of Brexit negotiations which were worrying and had huge implications for Ireland.
"In 2008, the then taoiseach Bertie Ahern went on a prolonged lap of honour while the country was on fire and I do not think it is appropriate for the current Taoiseach to do the same,'' he added.
"He should be reminded he is not just the leader of Fine Gael, he is also the leader of this country.''
Mr Ó Riordáin said while politicians were fascinated with the personality competition going on at the moment between various individuals in the Fine Gael party, what was happening in the country was much more important.
“What we need is a leader who can lead us into the Brexit negotiations and we do not need another lap of honour,’’ he added.
Fine Gael Senator Gabrielle McFadden said as far as most members of the party and herself were concerned there was no lap of honour.
“The Taoiseach has never sought that kind of admiration,’’ she added. “He has always put the country first.’’
Earlier, Independent Senator Gerard Craughwell congratulated the Taoiseach. "He went into a parliamentary party meeting of what appeared to be a divided party and he came out with a united party behind him,'' he added.
“That was some achievement and he deserves to be congratulated on it.’’
Mr Craughwell said he was glad Mr Kenny would be given time to leave office at his own bidding.