Independent deputy Michael Healy-Rae has said himself and his brother met Taoiseach Enda Kenny for "over an hour" yesterday.
Speaking on RTÉ's Late Late Show, Mr Healy-Rae said all of those elected had a duty to help form a stable and representative government.
He said that in order to support a particular party there would have to be a pledge in place to create a "senior minister for rural affairs".
However, Mr Healy-Rae declined to discuss the detail of his meeting with Mr Kenny any further.
Michael Healy-Rae topped the poll in the Kerry constituency and received the largest number of first preference votes nationally, while Danny Healy-Rae was elected on the second count in the same constituency.
