Fianna Fáil and Fine Gael are scheduled to recommence meetings with Independents and smaller parties at Leinster House on Tuesday, as both large parties seek to build support in advance of the next vote for taoiseach on April 6th.

Though most members of the cabinet are away on St Patrick's Day duty this week, a number of ministers – including Minister for Health Leo Varadkar, Minister for Agriculture Simon Coveney and Minister of State for Finance Simon Harris – have remained in Dublin to hold meetings with groups of Independents, individual deputies and the Social Democrats.

The acting Taoiseach Enda Kenny returns from a shortened Washington programme on Wednesday when he will be updated on the contacts, before flying to Brussels for a European Council meeting on Thursday.

Mr Coveney and Mr Varadkar differed on Monday on whether Fine Gael could support a minority Fianna Fáil administration. But a third cabinet member, Minister for Jobs Richard Bruton, said a minority government led by either Fine Gael or Fianna Fáil would have to had assurances from whichever large party was in opposition that it would be allowed to govern and implement its programme.

A number of Fianna Fáil TDs now privately say that supporting a Fine Gael minority government from opposition, on the basis of a broad agreement between the two parties, is the likeliest way forward.

Opposition within Fianna Fáil to a full blown coalition remains extremely strong, some TDs say. One deputy said that while grassroots members acknowledge there must be some co-operation with Fine Gael, they are still strongly against coalition.

The statement by Mr Varadkar that Fine Gael will not support a Fianna Fáil minority government was seen as significant.

“Fine Gael won’t back us in a minority government – that’s the bottom line,” said one deputy, who said that a two year agreement between the parties is a strong possibility. Such an arrangement would be acceptable to grassroots members, the source added.

Mr Coveney is due to meet rural-based members of the Independent Alliance in Athlone on Tuesday evening. Other meetings are expected to take place in Leinster House on Tuesday and Wednesday.

One Fine Gael Minister said the meetings were important in finding common ground with Independents and the Social Democrats, but that ultimately contacts would have to be opened with Fianna Fáil if there was to be any prospect of a government.

“Both parties accept that they can only lead a government with Independent support and also support from the other party,” the Minister said.

Fianna Fáil is also to hold meetings with the Social Democrats on Tuesday and with the Independent Alliance on Wednesday, while meetings with individual independent TDs will also continue over the coming days.

However, there is scepticism in Leinster House that anything substantial will be agreed between either party and the Independents and small parties before the Dáil next votes on the election of a taoiseach on April 6th.

The Dáil is due to meet on Tuesday, March 22nd, when the acting Taoiseach has promised to update the House on efforts to form a government, and for statements on housing, agriculture and on the European Council meeting.