Greek voters cast their ballots on Sunday in the country's first national election of the post-bailout era, with leftist Prime Minister Alexis Tsipras's Syriza party expected to be ousted by the conservative opposition.

After nearly five years in power, Greece's longest-serving crisis premier - as well as the youngest in more than a century - is battling to overcome a 10-point deficit in opinion polls amid widespread dissatisfaction after years of high taxation. 

Polling stations opened at 7 am local time and were set to close at 7 pm with 9,903,864 Greeks having the right to vote, according to the Athens News Agency. 

With three new opinion polls predicting a clear victory for the conservative New Democracy party, Tsipras called for supporters to mobilize, hoping for a turn around.

"Today we are fighting this battle from the first to the last minute. With optimism and determination. The ballots are empty and all possibilities are open," he tweeted on Sunday. 

After voting in Kypseli, near the center of Athens, with his supporters cheering, the premier called on young people "not to leave this crucial decision for their lives in the hands of others."

Opinion polls have consistently forecast that New Democracy headed by Kyriakos Mitsotakis, a former banker and scion of a leading Greek political family, will win an absolute majority in Sunday's legislative elections.

"Today is a big celebration of democracy. Greek women and men hold the fate of this land in their hands," Mitsotakis said after voting in an Athens suburb. 

Some members of a small far-left party protested outside the polling station where Mitsotakis voted, but their shouts were drowned out by New Democracy supporters calling their leader the new prime minister.  

"I hope that from tomorrow we will be able to breathe with relief. To take a deep breath. If Mitsotakis does what he promises," Athinodoros, a 48-year-old self-employed worker voting in Athens told AFP.        

Tsipras has accused Mitsotakis - who was part of a 2012-14 crisis government - of "disastrous" mismanagement that brought hundreds of thousands of job losses and business failures. According to the latest polls, New Democracy is expected to gain between 151 to 165 seats in the 300-seat parliament. Syriza meanwhile is forecast to fall from 144 seats to between 70 and 82.

Tsipras called the snap election in June after losing both European and local elections to Mitsotakis' New Democracy in the space of two weeks.