Some 3.1 million voters are eligible to elect 160 members to the 33rd Dail.
In the last major survey of the electorate before polling day, Sinn Fein was leading the popularity stakes on 25 per cent, with Fianna Fail second on 23 per cent and Mr Varadkar's party on 20 per cent.
Sinn Fein's struggle for a united Ireland has been on the back burner during the election, but the party is calling for a referendum on reunification within five years. "It's a three-horse race, three games, all within walking distance of each other".
Varadkar, 41, was the face of Ireland during the talks, which were crucial to Ireland because it is the only European Union country that shares a land border with the U.K. While most people applaud his success in securing guarantees that people and goods will continue to flow freely between Ireland and the north, the prime minister has had difficulty persuading voters that he needs another term in office to cement those gains in the next round of talks with Britain.
Both Fine Gael and Fianna Fail say they will build more houses, ease hospital overcrowding and cut waiting times for medical treatment.
Varadkar acknowledged that he understood that on Friday. "You want us over the next three years to focus on issues like health and housing with the same passion and intensity that we've focused on Brexit in the past three years", he said.
But, despite Brexit and historic votes to repeal strict abortion laws and introduce same-sex marriage, some predict that it could be dating.
The 2020 general election in Ireland kicked off at 7:00 a.m. local time (0700 GMT) on Saturday morning as scheduled, with the participation of a record number of female candidates, local media reported. The count starts at 09:00 GMT on Sunday with some expected results from the afternoon.
Surging support for Sinn Fein, which is committed to the reunification of Ireland, threatens the country's political equilibrium even though the party is unlikely to form the next government because both Fine Gael and Fianna Fail refuse to work with it.
Fine Gael's traditional rival Fianna Fail was the main party in government when Ireland experienced an economic collapse over a decade ago.
However, Vardakar was forced to hold elections in December when relations with FIanna Fail chief Micheal Martin and several independent lawmakers were required for a majority in the Irish Parliament's Dail Éireann.
"The only part that can lead an alternative government is Fianna Fail", he said in his hometown, Cork.
The brutal killing, and Sinn Fein's response to it, has become a major issue in the Irish General Election campaign.
"We are seeing a version of what we have seen elsewhere, a growing constituency, particularly among younger voters and those who feel forgotten that the neoliberal agenda has not worked for them", Farrell said.
Recent polls have suggested Sinn Fein gaining ground, prompting the larger parties to remind voters of the party's ties to past violence.
"We just need a change in Ireland, it's very obvious", said Eilis Wall, a 40-year-old preschool owner who traveled 200 kilometers (125 miles) to Dublin from western Clare County on Wednesday to join thousands of care workers Children asking for better state funding.
"This is a very hard situation as there is a family grieving - I don't want to add to their grief".