* Radical left believes it can govern alone
* Minister cool on post-poll deal with pro-bailout parties
* Greece must avoid second round of elections - Skourletis
* Breakaway party appeals for more defectors
By George Georgiopoulos and Renee Maltezou
ATHENS, Aug 25 (Reuters) - Greece's radical left Syriza party can win re-election with an outright majority, a senior member said on Tuesday, governing without support from mainstream forces which also back the country's new international bailout.
Panos Skourletis, energy minister in the Syriza-led government which resigned last week, also said the nation must avoid deadlock leading to a second round of elections - a scenario that politicians are already debating even though a first round has yet to be called.
Syriza, which during its seven months in power took Greece to the brink of financial collapse and exit from the euro, is projecting confidence, although it remains beset by internal divisions even after it formally split last week.
"I believe that an absolute majority in parliament for Syriza is achievable," Skourletis told Mega TV. He also played down the possibility of doing a post-election deal with the main pro-bailout groups - the conservative New Democracy, centrist To Potami or the PASOK socialists.
"For collaborations to be politically credible, they must be based on an existing convergence of programmes, a common ground," he said. "I do not see this political credibility with the forces of New Democracy, Potami or PASOK."
Greece's president has tasked two opposition parties with trying to form a new government after Prime Minister Alexis Tsipras quit last Thursday, hoping to avoid an election only seven months after the last one brought Syriza to power.
With parties deeply divided over the bailout - Greece's third since 2010 - and its tough conditions, New Democracy has already failed to find coalition partners.
Now Popular Unity, the far-left breakaway from Syriza, is going through the motions. Its leader, Panagiotis Lafazanis, has already admitted defeat and is using his three-day presidential mandate merely to win air time for his anti-bailout message.
Once his mandate expires on Wednesday night, President Prokopis Pavlopoulos is expected to make one final attempt to achieve a compromise among the parties. As this is also nearly certain to fail, he will then appoint a caretaker premier and call elections within 30 days.
Greeks are starting to worry the election might fail to end the paralysis just as the country is supposed to be implementing the bailout measures, and a second round must be held, as in 2012.
Skourletis opposed such a scenario. "We must avoid this. Some things have their limits. People know this and will vote in such a way so that we do not end up in a jam," he said.
Whether Syriza's show of confidence is justified is unclear. No opinion poll has been published since July 24, well before Tsipras resigned and Syriza split. Pollsters say it is hard to muster a representative sample when many voters are on holiday. However, most are now returning to the cities and polls are expected to start appearing shortly.
Syriza is banking on the assumption that Tsipras remains popular for standing up to Greece's euro zone and IMF creditors, even though he eventually caved in and accepted their demands for more austerity and economic reforms in return for 86 billion euros ($99 billion) in bailout loans.
But if Tsipras wants to jettison the hard left, leaving Syriza as a party a little closer to the centre that accepts the bailout, he has work to do.
Altogether 43 out of 149 Syriza lawmakers rebelled earlier this month by refusing to back the bailout in parliament. But only 25 subsequently formed Popular Unity, meaning Tsipras has to deal with a sizeable number of anti-bailout lawmakers who remain in Syriza.
These include the speaker of parliament Zoe Konstantopoulou and former finance minister Yanis Varoufakis.
Popular Unity appealed to Syriza doubters to defect. "Being pro-bailout and anti-bailout in the same party cannot go on," said Costas Lapavitsas, a former Syriza lawmaker who joined the breakaway.
"The third bailout is from the same womb as the previous ones. It will bring austerity and recession with a rise in unemployment," Lapavitsas, an economist who argues Greece would be better off leaving the euro, told Mega TV. ($1 = 0.8648 euros) (writing by David Stamp; Editing by Dominic Evans)