Mr Varadkar was in Ennis, Co Clare, where he expressed confidence his party would be returned on top despite recent opinion polls which have indicated a surge in support for Fianna Fail and Sinn Fein.
Across 39 constituencies, voters will choose from among 531 candidates including the incumbent Irish Prime Minister and leader of the former governing party Fine Gael, Leo Varadkar.
O'Malley ruled out Sinn Fein entering an alliance with Fine Gael but said an uneasy coalition between Fianna Fail and the republicans could theoretically be formed. It has a margin of error of plus or minus one percentage point.
Sinn Fein leader Mary Lou McDonald voted in central Dublin.
But Sinn Fein, which has appealed to younger voters on the defining issue of the election - the cost and availability of housing - has put forward too few candidates to capitalize, as the groundswell of support caught the party itself off guard after it sunk to 9 per cent at local elections previous year. His minority government has concluded a "trust and supply agreement" with arch-rival Fianna Fail, which gives it the votes it needs to decide on measures by topic.
No party is expected to reach the 80-seat threshold to enable it to govern on its own and a coalition administration of some complexion is nearly inevitable.
The second day at the Nemo Rangers GAA Club in Cork Ireland
However, Brexit did not feature prominently in his campaign that was instead dominated by domestic issues such as spiralling rental prices, record-breaking homeless numbers, controversy over the state pension age and a struggling health service.
However, David Farrell, a professor of politics at University College Dublin, told the Reuters news agency that the elections could be critical for Sinn Fein, which moved younger voters on the decisive issue of the elections: cost and availability of housing.
Varadkar launched his campaign after successfully helping to broker a deal cushioning Britain's European Union exit on January 31 by avoiding a hard border with British-run Northern Ireland. Sinn Fein's ultimate aim is to unify Ireland and British-run Northern Ireland, where it shares power.
In the weeks after his killing, Conor Murphy, a senior Sinn Fein figure claimed Mr Quinn was involved in criminality before his death. McDonald, a 50-year-old Dubliner, has helped Sinn Fein shed its hard-line image since replacing Gerry Adams, a Belfast native who led the party from 1983 to 2018.
Despite his leadership in the opinion poll, Sinn Fein, who wants to unite Northern Ireland with the Republic, is only presenting 42 candidates and can not form a majority government, even if everyone wins.
The shape of the government could take much longer to come into focus and may hinge on inter-party negotiations once the seat spread becomes clear.
But Brexit looks likely to nudge Northern Ireland's economy closer to that of its southern neighbor, and could yet increase pressure for a vote on unification.