Greek conservative Prime Minister Kyriakos Mitsotakis on Monday called for new elections "possibly on June 25", a day after securing a broad but inconclusive victory.

"We will head for new elections... as soon as possible," he told President Katerina Sakellaropoulou, adding that there was no possibility of forming a new government under the current parliament.

The conservative New Democracy party of Mitsotakis scored a thumping win in Sunday's vote, with a clear 20-point lead over its nearest rival -- Syriza led by leftist Alexis Tsipras.

Voters handed the conservatives their best result since 2007, crediting the party with bringing economic stability back to a nation once known as an EU laggard.

But the win fell short of an outright majority, leaving Mitsotakis with the option of either seeking a coalition or calling a new vote.

Left-wing daily Efsyn on Monday was headlined "Shock and awe", a feeling shared by both New Democracy and Syriza voters, while pro-government Proto Thema noted that the double-digit divide was the widest seen in the country since 1974.

Mitsotakis himself said the "great victory surpassed our own expectations".

With the count almost complete, New Democracy won 146 seats in the 300-deputy parliament -- five short of a majority.

The 55-year-old Harvard graduate on Sunday made clear his preferred option for a new ballot.

"Together we will fight as of tomorrow, so that in the next elections, what citizens have already decided -- a self-reliant New Democracy -- will be mathematically confirmed at the ballot."

"We will move forward, boldly and steadily, to complete today's important first step, and be the final winners," he said, adding that Greeks "want a strong government".

Tsipras also set the stage for a new vote, now expected as early as June 25, saying "the electoral cycle is not over yet".

The next battle, he said, will be "critical and final".