The leader of Greece’s far-left is to try to form a government after parties backing an international bailout deal failed to assemble a coalition.
Alexis Tsipras aims to put together a cabinet that will reject austerity measures imposed as part of the deal.
But analysts also say his attempts, following Sunday’s poll, are likely to fail to achieve the necessary numbers.
Voters in Greece, France and Italy have all largely swung in favour of anti-austerity candidates this week.
In Greece, both the centre-right New Democracy and former coalition partners Pasok, the traditional parties of power, saw their support drain away in favour of radical parties on the left and right.
France’s President-elect, Socialist Francois Hollande, said in his victory speech that he would seek an alternative to austerity.
And partial results from local elections in Italy suggest a marked swing away from mainstream parties. An anti-euro protest movement led by comedian Beppe Grillo made significant inroads in Parma and Genoa.
Reacting to the election results, German Chancellor Angela Merkel said austerity measures were “not negotiable” and described Greece’s reforms as of “utmost importance”.
Markets slumped following the election results in France and Greece, but largely recovered later. The Athens stock exchange, however, had plunged 6.67% by the end of Monday.
In return for two EU/IMF bailouts worth a total of 240bn euros (£190bn; $310), Greece agreed to make deep cuts to pensions and pay, raise taxes and slash thousands of public sector jobs.
Mr Tsipras, who heads the Syriza group, will on Tuesday be officially given three days to negotiate a coalition by President Karolos Papoulias.
The 38-year-old party leader has already promised to stitch together a left-wing cabinet to reject the “barbaric” measures associated with the bailout deal.
“We will exhaust all possibilities to reach an understanding, primarily with the forces of the left,” Mr Tsipras said.
But the numbers just do not seem to add up, the BBC’s Matthew Price in Athens says.
Earlier on Monday, New Democracy leader Antonis Samaras admitted he had failed to find a coalition cabinet, stressing that his party had done “everything possible” to form a government.
“I tried to find a solution for a government of national salvation, with two aims: for the country to remain in the euro and to change the policy of the bailout by renegotiation,” he said in a televised address.
“We directed our proposal to all the parties that could have participated in such an effort, but they either directly rejected their participation, or they set as a condition the participation of others who did not accept.”
If Mr Tsipras fails to clinch a coalition deal, the mandate then passes to Pasok leader and ex-finance minister Evangelos Venizelos.
Mr Venizelos said Syriza and the smaller leftist party of Fotis Kouvelis should be involved in any new coalition.
“It is necessary for the government of national unity to include all the forces that have a pro-European outlook,” Mr Venizelos said. “The minimum level of agreement is that Greece remains in the euro.”
Snap elections will be called if no agreement is found, with analysts saying the polls could be held in the summer.
Despite emerging as the biggest party, New Democracy’s support slipped from 33.5% in the last election to less than 19% on Sunday.
Support for the centre-left Pasok, which also supported the austerity measures, plummeted from 43% to just over 13%.
Syriza took 16.8%, while fellow anti-bailout party, the ultra-nationalist Golden Dawn, won almost 7%.
The financial chaos has sparked huge social unrest, and led to a deep mistrust of the parties considered to be the architects of austerity.