Estonian MPs are choosing between former European Commissioner Siim Kallas (Reform Party), Eiki Nestor (Social Democrats), Mailis Reps (Center Party), Mart Helme (EKRE), and Allar Jõks (IRL/Free Party).
On Monday, no candidate received the required two-thirds majority (68 out of 101 possible votes) in the secret ballot, which now means a second and third round of votes on Tuesday.
Estonia's ruling three-party coalition has been divided over who should become the next President, a mostly ceremonial post.
One of the favourites standing to replace Toomas Hendrik Ilves as President had been Kallas, a former Estonian Prime Minister and European Commissioner.
Ilves is a former MEP whose second and final term expires in October.
Between 2004 and 2014, Kallas held three separate briefs as Commissioner. Before his career in Brussels, Kallas held many of Estonia's senior government posts, including Prime Minister (2002-2003), minister of finance (1999-2002), and minister of foreign affairs (1995-1996). He has also been President of the Bank of Estonia (1991-1995).
For some Estonians, Kallas' domestic political career gives him the reputation of a competent senior statesman, while his extensive experience at the EU-level has added to his international status.
Kallas forged his early political career as a member of the Communist party, holding a number of prominent positions in Soviet Estonia before 1991.