It comes as the Irish Prime Minister Leo Varadkar warned that Brexit was entering a "very dangerous" phase following Theresa May's resignation.
Irish Prime Minister Leo Varadkar's staunchly pro-EU Fine Gael party was seen in the lead in European elections, according to an exit poll on Friday, after a campaign dominated by concerns about Brexit.
Centre-right Fine Gael candidates were ahead in two of Ireland's three constituencies, with the Greens coming first in Dublin, the poll of about 3,000 voters conducted by TV channels RTE and TG4 in Dublin suggested.
As he cast his vote in Dublin earlier on Friday, Mr Varadkar warned that Brexit was entering a "very dangerous" phase following the resignation of Prime Minister Theresa May as a more hardline politician could replace her.
"But whatever happens, we're going to hold our nerve.
"We're going to continue to build and strengthen and deepen our alliances across the European Union and we'll make sure that we see Ireland through this," he said.
It comes on top of an exit poll in the Netherlands on Thursday that indicated Dutch parties also committed to the EU were likely headed for a surprise win.
Those early indications undermined to a degree coverage before the start of the four-day contest across the EU that spoke of a possible rise of anti-establishment parties.
More than 400 million people are eligible to elect 751 MEPs continent-wide, with the first official results to be announced late Sunday once voting in all 28 member states has been completed.
The Netherlands and Britain, where Prime Minister Theresa May finally announced her departure Friday following a months-long Brexit crisis, kicked off voting on Thursday. Italy will be the last country to close polls late on Sunday.
Turnout will remain a major concern in the EU vote that has sparked little enthusiasm since its first edition in 1979, with eastern Europeans historically the least motivated to go to the polls.
Authorities are also concerned by disinformation campaigns on social media by outside actors - notably Russia - trying to influence the outcome.
Activists say Facebook has closed news pages and scrapped accounts in its effort fight back fake news and avoid the embarrassing scandals that followed the US election of Donald Trump in 2016.
Around the continent, pro-European leaders are seizing on the surprise in the Netherlands to mobilise their supporters to resist a populist gain, with opinion polls indicating nationalist parties lead in France, Italy and Hungary, among others.