"I expect serious fight in the runoff and I'm ready to do that," he told journalists after casting his vote in Vilnius District.
Accompanied by his wife Silvija and children, the prime minister refrained from commenting on whether he would stand down as prime minister if he failed to get into the presidential runoff, adding that decisions would be made after the election results.
"I don’t speak about that now. Let's wait for the results and then we'll consider what will be next," the prime minister said, also adding that he voted in both ongoing referenda and called on people to do the same.
Skvernelis is running for Lithuania's president against European commissioner Vytenis Povilas Andriukaitis, MP Ingrida Simonyte, representing the opposition conservative Homeland Union – Lithuanian Christian Democrats, philosopher Arvydas Juozaitis, MEP Valentinas Mazuronis, economist Gitanas Nauseda, MPs Mindaugas Puidokas and Naglis Puteikis and Valdemar Tomasevski, leader of the Electoral Action of Poles in Lithuania – Christian Families Alliance.
Polls show no candidate is likely to get more than 50 percent of votes and runoff voting will be necessary in two weeks, involving two candidates with the most votes.
The term of incumbent Lithuanian President Dalia Grybauskaite ends in July.
Lithuanians are also voting in two referenda on Sunday.
In the referendum on amending Article 55 of the Constitution, citizens are voting on whether or not to reduce the number of Seimas members to 121, from the current 141.
In the other referendum, they are voting on whether or not to amend Article 12 of the Constitution so that Lithuanian citizens by birth do not lose their Lithuanian citizenship when they acquire the citizenship of another country meeting Lithuania's European and transatlantic integration criteria.
During early voting this week and the first hour of voting on Sunday, 11.52 percent of voters have expressed their will.