About 9.8 million Greeks began voting at 7 a.m. local time with a close contest expected between the radical leftist Syriza party, which wants to scrap a European financial bailout, and the New Democracy conservative party, according to Agence France-Presse.
Recent opinion polls have placed Syriza equal in popularity with New Democracy.
The poll is a re-run of the general election on May 6 that ended with the political parties failing to form a coalition government.
Barack Obama and Angela Merkel are among world leaders who have urged voters to support the bailout, as a loan freeze would further imperil Greece's weakened economy, Australia's ABC reported.
The European Union and International Monetary Fund insist that the conditions of the 130 billion euro ($164 billion) bailout deal — including tough austerity measures — must be accepted in full by a new government or funds will be cut off, driving Greece into bankruptcy.
Syriza leader Alexis Tsipras vowed to tear up the deal, agreed in March, and says he will renegotiate with creditors from scratch, AFP reported.
New Democracy leader Antonis Samaras wanted to renegotiate aspects of the deal, however said rejection of the EU/IMF bailout would mean a return to the drachma and even greater chaos, the Irish Times reported.
A favorable result for New Democracy would lift European markets, while a result that saw Syriza leading a government would spark a selloff, Barrons wrote.
Greeks have consistently expressed their desire to remain part of the euro zone, according to Barrons.