The 50-year-old said she ideally wanted "a government with no Fianna Fail or no Fine Gael in it" and had made contact with smaller parties, but added: "I will talk to and listen to everybody". Fianna Fail received 22.2 percent of the votes.
Incumbent prime inister Leo Varadkar's governing Fine Gael party won 20.9%.
"I want us to have a government for the people".
The left-wing Sinn Fein shocked the country when it emerged as the most popular party in an opinion poll released on Monday, with 25% of support, up from 14% support in the 2016 vote.
"It is something of a revolution in the ballot box", McDonald told reporters after arriving at her election count to a huge ovation from party supporters. Ireland uses a system of proportional representation but also includes preferential voting, meaning that first-choice votes could be shifted to other candidates and translate to a different proportion of seats. Sinn Fein stood on 37, Fianna Fail on 36 and Fine Gael on 35, with Fianna Fail hopeful of winning the final two seats. But forming a stable alliance looks tough.
Instead Varadkar's Fine Gael is likely to compete with fellow centre-right rival Fianna Fail to secure the most seats and the right to try to form a coalition government - a task analysts called extremely hard.
"This election has certainly been seismic and historic, it's been an election that's really been driven by a demand for change by the people", she said.
'If you ask me when that is, I think it's probably five years off at least.
Ireland could be without a stable government for months if the country's three big political parties do not manage to form a coalition.
The election could be most pivotal for Sinn Fein, which has moved on from the long leadership of Gerry Adams and is run by a new generation of politicians led by Mary Lou McDonald.
A Fine Gael or Fianna Fail-led government "would largely mean continuity from a financial and economic policy perspective", said Mr Bert Colijn, an economist with ING Groep NV.
The IRA was responsible for murders, bombings and other violence during decades of violence known as the "Troubles" in Northern Ireland.
If Johnson wants to implement a hard plan, 'the Irish backstop', envisioning a Northern Ireland which could stay within the United Kingdom customs union, but can still operate under EU regulations, it might take the British region closer to Dublin than London, angering pro-British Protestant Unionists.
Sinn Fein's rise is being put down to the left-wing nationalist party running on an anti-austerity campaign, that focused on tackling the housing crisis by providing more social homes, as well as promising to deliver better healthcare.
Yet many party members, particularly in Dublin, are queasy about bringing Sinn Fein in from the cold and risking alienating the party's middle class support base.
Journalist Ruth Dudley Edwards, in her column in the Belfast Telegraph, wrote: "This reminds many who know Sinn Fein as puppets of the IRA Army Council of Germany in 1932, when the Nazi party became the largest in parliament: Hitler became Chancellor in January 1933 and wasted no time in establishing his brutal dictatorship.""It is classic populism".
LEO VARADKAR's election nightmare went from bad to worse after he became the first sitting Taoiseach in Irish history not to top the poll in his own constituency.
Ireland held a general election on 8 February, just one week after neighboring Britain's departure from the European Union.
"The government handled the Brexit as good as could be done, but that's over".
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