Political parties in Ireland are continuing the slow, steady process to form a government in the new year.

The most likely coalition partners are Fine Gael and Fianna Fail – along with several independents making up the handful of remaining seats needed to form a majority.

Fianna Fail and Fine Gael both said they had a “positive and constructive” initial discussion on Wednesday about a programme for government.

A further meeting between the two parties is being held on Thursday.

Despite momentum being behind the Regional Group as a junior coalition partner, which has eight independent TDs, the Labour Party and the Social Democrats have not officially ruled themselves out of the discussions.

The Social Democrats said they would continue engaging with Fine Gael and Fianna Fail, as well as main opposition party Sinn Fein and Labour, while Labour’s parliamentary party is to meet on Friday at 1pm.

Social Democrats deputy leader Cian O’Callaghan said the parliamentary party was told the formation talks had been “positive and constructive with a good exchange of views”.

“These talks have been exploratory to date but I expect that next week they will become more focused – particularly on the dealbreakers we highlighted during the election campaign,” he said in a statement on Thursday.

The party’s red lines include the delivery of 50,000 affordable homes during the next government’s term in office; the full implementation of Ireland’s plan for universal healthcare, Slaintecare; “quality” public childcare; a senior minister for disability and “credible” climate action.

Fianna Fail, which won 48 seats in the general election held two weeks ago, and Fine Gael, which secured 38 seats, headed up the last coalition and are expected to continue that partnership into the next mandate.

But with a combined 86 seats, they are just short of the 88 required for a majority in the Dail parliament.

Both Fianna Fail and Fine Gael have ruled out doing business with Sinn Fein, which won 39 seats.

Irish premier and Fine Gael leader Simon Harris said on Wednesday that it appeared to him that independents were “very serious” about being a part of government.

Neither he nor Fianna Fail leader Micheal Martin would be drawn on whether they would be the next taoiseach.

Mr Harris said ideally an Irish government would be formed before Donald Trump is inaugurated as the next US president on January 20.

Mr Martin said the “substantive” formation work would be completed before Christmas and he would be hopeful an administration would be in place before Mr Trump’s inauguration.

The new Dail parliament of 174 TDs is to sit for the first time next Wednesday.

The Regional Group is to nominate Wexford Verona Murphy for the position of speaker, known as Ceann Comhairle, which would make her the first woman to hold that position since the formation of the State if she is confirmed.

The three sides are to meet next week to discuss and agree the structure and parameters for engaging in Government formation talks, the Regional Group said.