The acting Health Minister says he does not think that changing Fine Geal's leader would make it easier to form a government.

A minority government now appears to be the only option, after Fianna Fáil yesterday rejected an offer for coalition.

Fine Gael's unprecedented offer remains, officially, on the table.

However, after its overwhelming rejection yesterday, both parties will now be attempting to put together the numbers for a credible minority administration.

Responding to the Fianna Fáil's rejection of the proposed 'full partnership' government offer, Enda Kenny said the decision was a “serious mistake” driven by "narrow party interests rather than the public interest".

As of this morning, neither the Independent Alliance of six TDs nor the Rural Alliance of five deputies have been invited to any further talks.

Those groups - and the four other independents who have attended talks - now represent the parties' only potential partners in government.

While it remains uncertain whether Fine Gael or Fianna Fáil can build the biggest platform, the support of the other would still be required.

Leo Varadkar says Fine Gael are still available to enter talks with Fianna Fáil on the formation of a partnership government - and that his party was anxious to put together a government that reflected the way people voted in the recent election. 

Speaking to Newstalk Breakfast, the acting Health Minister also said "a change of leader isn't going to change the arithmetic. The underlying difficulty as to why we're struggling to put together a government is the result of the election".

Anti Austerity Alliance TD Paul Murphy has said that Fianna Fáil's decision not to enter Government could be designed to put pressure on Enda Kenny.

Deputy Murphy said that fundamentally the parties policies are the same, but that the acting Taoiseach may be the sticking point.

"I do think they'll go back and forth on this minority government thing if they have to - fundamentally their ideas are not dissimilar at all," he added.