Greeks are voting for the second time in a month with conservative ex-Prime Minister Kyriakos Mitsotakis hoping to secure a big majority.
He convincingly beat his centre-left rival in May but called new elections in a bid to govern Greece alone.
Sunday's vote comes little more than a week after a migrant boat tragedy off the Greek coast in which 500 people are thought to have died.
But the disaster has had little effect on the campaign.
Mr Mitsotakis's conservatives won last month's elections by a 20-point margin over the centre-left Syriza party of Alexis Tsipras, another former prime minister, and he is confident of a repeat victory that would hand him a second term.
Voting continues until 19:00 (16:00 GMT).
Without a majority of more than 150 in the 300-seat parliament, Mr Mitsotakis says his New Democracy party cannot form the stable government that is necessary.
"In uncertain times, Greece needs a government that will not depend on fragile majorities," he told a rally in Syntagma square in central Athens on Friday night.
The big difference in Sunday's election is that the winning party is awarded up between 20 and 50 bonus seats, so a similar repeat victory would give him the mandate he wants.
Mr Mitsotakis is widely seen as having successfully returned the Greek economy to stability and growth after a severe debt crisis and three international bailouts. Although many Greeks are struggling with the cost-of-living crisis, voters last month chose to stick with the party promising lower taxes and improved public health.
He has formed a reputation as a Teflon-coated leader, fending off a series of damaging crises in the past year including a rail disaster and a wire-tapping scandal that brought down the intelligence chief and his own nephew, who worked as the prime minister's chief of staff.
His centre-left rival faces an uphill task. Alexis Tsipras told supporters in Thessaloniki that voters were being offered two different visions of Greece: "a country and society of humanity, democracy and justice" or a right-wing programme that put the profits of the view above the lives of the many.
The two leaders took very different approaches when a migrant boat sank off the south-west coast only 11 days ago.
The campaign came to an abrupt halt as Greece observed three days of mourning and questions have been asked about the response of the Greek coastguard in the hours before hundreds of people lost their lives.
Mr Mitsotakis has mounted a passionate defence of the coastguard and condemned the people smugglers as "scum".
Mr Tsipras did raise concerns, though.
He said that, at the time he was in charge during the 2015 European migrant crisis, when more than a million people travelled through Greece, the coastguard, police and military had all worked "with one objective, human life".
Since the migrant crisis, the views of most Greek voters have shifted in favour of stricter, more conservative policies, says Panos Koliastasis, assistant professor of politics at the University of Peloponnese.
"The reason is rooted in the 2020 migration crisis on the Evros [river], when Turkey tried to push thousands of migrants into Greek territory and the Mitsotakis government acted swiftly. So the greater part of the public perceives the migration issue as an external threat to national sovereignty."
Mr Mitsotakis is also benefiting from the fragmentation of the Greek left. As the debt crisis mounted in 2012, voters on the left gradually abandoned the old Socialist Pasok party in favour of Alexis Tsipras's more energetic style.
But Syriza's fortunes waned under a Tsipras government and the Socialists are now the third political force in Greece. Neither of the two left-of-centre parties will go into coalition with the conservatives.
The New Democracy leader is a rarity in Greek politics, having increased his share of the vote since the 2019 elections.
He also won the youth vote, with more than 30% of 17 to 34 year-olds, reaching out to voters on TikTok and other social media platforms.
Panos Koliastasis highlights a remark by Mr Mitsotakis last November in which he told journalists his 2023 election campaign began the day after he won in 2019.
"Hardly a day went by without Mitsotakis giving an interview, a press conference, a visit to some area or foreign travel," he says.
His focus on positive messages appeared to chime with Greek voters whose main concern was the economy and living standards, rather than inflation or the worst rail disaster in Greek history last February which claimed 57 lives, many of them students.
Source: BBC