"We're not going to blow up everything, " said Nikos Pappas, a senior Syriza official.
It's an uncanny repeat of the similar electoral success of the anti-establishment Syriza party in Greece.
Voters must choose between the so-called moderate-right New Democracy party or the so-called leftist Syriza party.
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Then, in the 2004 election, Synaspismos came together with other small parties to form Syriza.
Some KKE voters were saying they would switch votes to Syriza in a second election.
Even a Syriza victory will thus probably lead in the first place to negotiations.
Alexis Tsipras, the leader of the Syriza party, leads in polls ahead of the June 17 election.
Syriza could end up forming a government if New Democracy fails to do so within three days.
In the previous parliament, elected in 2009, Pasok held 160 seats, New Democracy held 91 and Syriza, 13.
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An official with Syriza told CNN that no one from the party was planning to attend the meeting.
CNN: Greek party official: Coalition talks to be held Tuesday
Already, large Greek firms are guarding against a Syriza victory by exploring how to move their listings abroad.
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As events pulled Syriza leftward and swelled its support, one final split took place that may prove highly significant.
An already hostile Greek media is asking if Syriza is a party that could ever run the Greek state.
Amid this, the challenge for Mr Tsipras's party, Syriza, is what would you do if you gained power?
Tsipras, the head of Syriza, which has vowed to cancel the bailout terms.
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Syriza's idealistic economic programme calls for providing students with free meals and doling out pensions equal to final salaries.
Pasok leader Evangelos Venizelos called for a national-unity government including the Democratic Left and Syriza as well as New Democracy.
Public support for Syriza, and Mr Tsipras, dipped when the opposition party publicly backed a tube strike that paralysed Athens.
Only ND can beat Syriza, and if it beats them with anything more than three points I will be surprised.
Additional pressure will come from opposition leftist bloc Syriza, which strongly opposes the tough austerity measures required under the bailout.
Syriza, which broke through to 17% in the May election, looks set to replace Pasok as the main opposition party.
In short, Syriza offers a blast from the past: failed strategies to keep hiring public workers and to isolate itself internationally.
What Syriza shares with the Dem Left and Pasok is its commitment to the EU social model: they are left globalists.
One current obstacle to this is the KKE's historic enmity to Syriza and indeed the entire rest of the Greek left.
But second-place Syriza will be a defiant voice of opposition, correspondents say.
This is not the only parallel with the rise of Syriza, the hard-left party in Greece that opposes that country's bail-out programme.
Syriza would cancel the Greek bailout agreements and presumably negotiate from scratch.
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It looks like investors are seeing a possible shift away from Syriza.
Syriza, which campaigned against the terms of the bailout, got 71 seats.
CNN: Greek party official: Coalition talks to be held Tuesday
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