With 1,631 of the country's 1,972 voting districts counted by early Monday, results provided by Lithuania's Central Electoral Commission show banker-turned-politician Gitanas Nauseda leading the nine-candidate field with 31.2% of the votes cast Sunday.
Lawmaker and former finance minister Ingrida Simonyte is second with 27.2%. A candidate needed to win more than 50% of the votes to avoid a runoff. Grybauskaite has served two maximum five-year terms as Lithuania's head of state since 2009.
Voters are going to the polls in Lithuania to elect a president to succeed Dalia Grybauskaite, who has completed her maximum two terms in office.
Nine candidates are taking part in Sunday's vote, which could require a runoff in two weeks' time.
The leading candidates include Prime Minister Saulius Skvernelis, former banking economist Gitanas Nauseda and former Finance Minister Ingrida Simonyte.
The campaign has focused on domestic issues such as the economy, corruption and social welfare, even though foreign policy and defense are two of the presidency's main purviews.
Grybauskaite's anti-Russia views, no-nonsense style and karate black belt earned her the "Iron Lady" label previously applied to Margaret Thatcher when she was British prime minister.
Voters are also having their say in a referendum on a constitutional amendment to allow dual citizenship for hundreds of thousands of Lithuanians living abroad.