The new leader of Fine Gael Leo Varadkar has held what has been described as a "positive and constructive meeting" this afternoon with his former challenger Simon Coveney.

The two ministers were said to have discussed "Minister Varadkar's plans for the party and the country".

There was no mention of what role Mr Coveney might play in Mr Varadkar's cabinet.

Upon election as taoiseach, Mr Varadkar will have to reshuffle Cabinet to a degree. There are at least two vacancies to fill including Michael Noonan's Finance portfolio and Mr Varadkar's own job as Minister for Social Protection.

Mr Noonan said recently that he did not wish to be considered for a Cabinet position by the new Fine Gael leader.

Mr Noonan, 73, said he will continue in his role until a successor is appointed.

Over the coming days Mr Varadkar will also hold talks with Fine Gael's partners in government and with Fianna Fáil next week.

He will also be contacting the independents that form the minority Government.

He has already spoken to Independent Alliance ministers Shane Ross and Finian McGrath but more formal engagements are due next week.

Mr Ross has indicated that the Alliance may raise new issues with the new leader.

Mr Varadkar will also have to engage with the other independent ministers in government, Denis Naughten and Katherine Zappone, while there are also two independent TDs - Michael Lowry and Michael Harty - who mostly vote with the Government although no formal agreements are in place.

Mr Harty set down a marker last week telling RTÉ he would have to consider his support for the new leader.

Mr Varadkar will also hold discussions with the main opposition party, Fianna Fáil, and has stated clearly that he will honour Fine Gael’s deal with Fianna Fáil, but he was adamant that he will not renegotiate it.

Fianna Fáil's Jim O'Callaghan said the party is anxious to reaffirm the 'confidence and supply arrangement' with Fine Gael.

David Cullinane of Sinn Féin said an election should be called to give the public an opportunity to vote on Mr Varadkar’s policies.