Former Greek Prime Minister Alexis Tsipras' leftist Syriza will emerge as the biggest party after next month's election but without the sizeable margin it was hoping for, the first major opinion poll since he resigned last week showed.

The survey also found that almost two thirds of voters felt Tsipras should not have sought a fresh mandate and that his favoured coalition ally would not make it into parliament.

That suggested his gamble to call early elections to consolidate his power base could backfire, though over quarter of voters remained undecided, making the final outcome far from clear.

Syriza was supported by 23 per cent of those polled, with the conservative New Democracy party second on 19.5 per cent, according to the survey, carried out by pollsters ProRata and published in Efimerida Ton Syntakton newspaper.

The previous ProRata poll in early July showed a wider gap in Syriza's favour, putting the party on 26 per cent compared with 15 per cent for New Democracy.

Tsipras remained the most popular political leader with 41 percent of voters having a positive or very positive view, with New Democracy leader Vangelis Meimarakis was not far behind with 34 per cent.

But 64 per cent of Greeks said they believed Tsipras's move to call snap polls was wrong, while 68 per cent agreed that Greece must stay in the euro zone at any cost, even if that meant further austerity.

"The answers to these two questions lead to the conclusion that early elections may cost the (former) prime minister and Syriza," the newspaper said.

The president is expected to confirm Sept. 20 as the election date.

A caretaker government led by Supreme Court judge Vassiliki Thanou was sworn in earlier, comprising both technocrats and political figures.