Greece's top judge on Thursday became the country's first female prime minister, taking over a caretaker administration to organise early elections next month, the fifth in the crisis-hit country in six years.

Vassiliki Thanou, the 65-year-old head of the Supreme Court, took her oath of office in a brief ceremony at the presidential mansion.

Dressed entirely in white, the diminutive judge then told outgoing PM Alexis Tsipras that her administration was likely to face additional challenges, such as the migrant wave from Syria.

"As the circumstances evolve, I feel this government will be called upon to face (other) critical issues such as migration," she said.

Tsipras said Greece was likely to have a discussion concerning relief on its soaring debt sooner than expected.

"Until now we knew that the discussion on debt reduction would be held by the end of the year," the outgoing PM said.

"Today we learned from Eurozone stability mechanism managing director (Klaus) Regling this will now be sooner, perhaps in October," he said.

Mother-of-three Thanou has taken a hard stance on austerity measures, having criticised as unconstitutional an unpopular property tax collected through electricity bills.

In February, she fired off an emotional letter to European Commission chairman Jean-Claude Juncker, protesting that austerity cuts were "annihilating" the Greek people.

"The people are not responsible for the waste of public money by past governments and for mistakes in tax policy," she wrote, adding that the austerity measures "have failed as the recession continues as the rich continue to evade taxes".

Thanou, who holds a degree in European law from France's Sorbonne university, will name her administration on Friday, the president's office said.

The date for Greece's general election is to be officially announced by the end of the week, but it is likely to be scheduled for September 20.

Tsipras has ruled out forming a national unity government should he fail to win a outright majority in the snap elections triggered after he resigned last week.

Tsipras called for the fresh vote on August 20 after suffering a major rebellion in his hard-left Syriza party over Greece's huge new international bailout, its third in five years.

But on Wednesday, he dismissed suggestions he could work with the conservative opposition New Democracy, the Pasok socialists or the centre-right Potami if the election results were inconclusive.

"If we do not have a majority, I will not cooperate with (the parties that ran) previous governments." Tsipras said in an interview with the Alpha TV channel, his first since resigning.

Bitterly divided

Syriza stormed to election victory in January on a wave of popular anger over tough austerity measures demanded by Greece's creditors in exchange for two previous bailouts since 2010.

But the party has been bitterly divided over Tsipras' decision to accept more tough reforms in exchange for a new 86 billion euro ($96 billion) rescue package, with hard-left rebels accusing him of capitulating to "blackmail" by the creditors.

On August 21, 25 Syriza rebels announced the formation of a new political grouping, Popular Unity, led by Panagiotis Lafazanis, a former senior Communist who has argued that Greece can happily exist without the euro.

"We are the true continuation of Syriza and its electoral pledges," Lafazanis said on Thursday.

Tsipras remains popular, although in the absence of recent opinion polls it is difficult to know whether he could win an absolute majority in the forthcoming poll.

The 41-year-old leader's opponents had sought to delay the election, hoping that voters will be less likely to vote for Syriza once the new austerity measures begin to bite in the autumn.

Lafazanis strongly criticised on Thursday the president's decision to skip a meeting of political leaders that had no chance of producing a government, opting instead to talk to each leader by telephone.

"The constitution makes no reference to phone calls," Lafazanis said.

One of the government's former stars, ex-finance minister Yanis Varoufakis told Australia's ABC that he would sit out the election campaign which he described as "sad and fruitless".

"I think we should try to aim for a European (anti-austerity) network that at some point evolves into a pan-European party," he said.

The EU has taken the snap ballot decision in its stride, and debt rating agency Moody's has even called Tsipras' resignation "credit positive," arguing that it could well create a more cohesive government.