The two main centre-right parties in Ireland are expected to start talks on returning to government as the general election put the incumbents within touching distance of forming the 34th Dáil.

With all Teachta Dála (TD) seats filled by 10pm on Monday evening, Fianna Fáil – led by Micheál Martin – and Fine Gael – led by the taoiseach, Simon Harris – won 86 seats, just two shy of the 88 needed for a majority.

Sinn Féin were slightly ahead of Harris’s party with 39 TDs and had opened talks with the Social Democrats and Labour, both taking 11 seats each. However, with Fianna Fáil (48 TDs) and Fine Gael (38) ruling out a coalition with the leftist national party, a left-leaning alliance is unlikely to materialise.

With Fianna Fáil now 10 seats ahead of Fine Gael, Harris’s position as taoiseach is likely to come under pressure.

If it is to be a direct reprise of the Fianna Fáil-Fine Gael governing partnership of the last mandate, one of the major questions is whether the parties continue their policy of rotating taoiseach, or prime minister. The previous coalition struck a historic agreement to have first Martin and then Leo Varadkar, the then leader of Fine Gael, followed by Harris, serve as taoiseach.

Fianna Fáil’s deputy leader, Jack Chambers, said on Monday talks could last for weeks but not the near-five months it took for their coalition with Fine Gael to crystallise last time.

“I don’t expect the government to be formed in mid-December,” he told RTÉ, adding that time was needed to discuss negotiations within the party and the space to form “a coherent, stable” arrangement.

The Sinn Féin leader, Mary Lou McDonald, has already reached out to the Social Democrats and Labour.

Subsequent results showed the party with a 19% share. While it will remain the single biggest opposition party, it represents a significant fall on its 25% share four years ago.

Eoin Ó Broin, one of the most senior members of the party, said the party would meet on Wednesday where it would “assess” where it would “take things at that stage”. Other party members have said they will try to form a leftist block and make it as “difficult as possible” for another term for Fine Gael, which has been in power since 2011.

The final results were: Fianna Fáil, 48; Sinn Féin, 39; Fine Gael, 38; Independents, other, 21; Social Democrats, 11; Labour, 11; People Before Profit, three; Aontú, two; and the Greens with one.

The pivotal decision for Fianna Fáil and Fine Gael centres on whether the two parties team up like-minded independent candidates to form the next government or whether they rely on the support of either of the smaller left-leaning parties, the Social Democrats or Labour.

Agreeing a programme for government after a campaign that involved big spending promises will involve much horse-trading but all parties are agreed they must deliver on housing and homelessness, the number one priority of the electorate, according to Friday night’s exit poll.

Chambers said his party would seek to prioritise its promises. “This isn’t about positions or posturing or general groupings. It’s about how we can deliver for the Irish people,” he told RTÉ.

The government’s previous partner, the Greens, were virtually annihilated in the election with its leader, Roderic O’Gorman, the sole remaining TD of 12. After scraping in on the 13th count in Dublin West constituency on Sunday night he said he did not think he had a mandate to return to government.

The two establishment parties have already ruled out working with Sinn Féin, which is expected to finish with a similar number of seats as Fine Gael but not enough to lead a stable left-leaning government.

Labour and the Social Democrats have both said they would talk to Fianna Fáil and Fine Gael but would first take stock of the position of parties on the left.

Ivana Bacik, the Labour leader, described her party’s results as “formidable” given only four sitting TDs had sought re-election.

She told RTÉ she would not consider “going it alone” into a coalition with the two big parties and they wanted to assess the position of the “TDs who share our vision and our values who want to deliver change” including delivering housing, public services, healthcare, childcare and disability services.

“We are serious about delivering change and that’s why we have talked about forging a common platform,” she said. The first people she would talk to are the Social Democrats and O’Gorman, she said.

The Social Democrats have also said they are prepared to talk to the established parties but have five red lines, including the demand for a disability minister.