* Conservative Anastasiades short of outright majority
* Run-off against Communist-backed Malas on Feb. 24
* Kingmaker Lillikas suspicious of terms for any bailout
* Financial crash could reignite euro zone crisis
* Runner-up will say on Friday who he supports
NICOSIA, Feb 18 (Reuters) - The Cypriot politician most in favour of an international bailout was in pole position to win next Sunday's run-off presidential vote as he and his communist-backed rival launched a week of bargaining to woo voters suspicious of a rescue package to stave off bankruptcy.
Conservative leader Nicos Anastasiades, who backs a swift deal with the European Union and International Monetary Fund on a bailout to fight the worst recession in four decades, faces off Stavros Malas in a second-round vote on Feb. 24 after neither won a clear victory in the first round on Sunday.
Markets are looking at a stalemate over Cyprus getting aid with growing alarm, fearing a debt default could reignite the euro zone debt crisis just as confidence slowly returns.
Both candidates need to broaden their appeal to woo supporters of third-placed finisher George Lillikas, an independent who has said the terms of any bailout could keep Cyprus in perpetual bondage to foreign lenders.
He took a surprisingly high 25 percent of the vote, just two points behind Malas. Anastasiades, 66, took 44.5 percent, 15,000 votes shy of an absolute majority that would have spared him the need to fight a second round.
Lillikas kept candidates guessing about his intentions on Monday, saying he would consult his supporters. "After concluding this dialogue I will announce my position," he told journalists.
He said that would be on Friday, a day after Socialist EDEK party, which had endorsed Lillikas, was due to announce its own recommendation for the second round. Both run-off candidates had meetings scheduled with the EDEK leadership on Tuesday.
Lillikas has expressed misgivings about potentially onerous terms of a bailout deal with international lenders, saying Cyprus should negotiate hard to be able to extricate itself from bailout terms as soon as possible.
He has floated the idea of securitising Cyprus's natural gas reserves, a proposal which has little traction with the other two candidates who say it is premature. Exploration of those offshore reserves is still incomplete.
He has long been critical of Anastasiades over the latter's support for a U.N. reunification plan for Cyprus in 2004 - unforgivable in the eyes of many hardline Lillikas supporters.
However, Malas is backed by Communists, who Lillikas says conceded too much to Turkish Cypriots in peace talks when in government.
Next Sunday's winner will replace President Demetris Christofias, a Communist Anastasiades has charged with running the economy to the ground. Christofias is not seeking a second term.
If successful, Anastasiades faces a long list of challenges in convincing the European Union and International Monetary Fund to sign off on a rescue before the tiny state faces a 1.4-billion euro debt repayment in June.
He will have to assuage fears that Cyprus will never be able to pay back its debt even if given a bailout loan equivalent to the size of its economy, and quell concerns in northern Europe that the island is a hub for laundering money from Russia.
Talks on a rescue, which have dragged on for eight months, have also proven tricky because almost any way of solving the crisis - from restructuring debt to imposing losses on banks - could set a precedent for other troubled states and damage sentiment just as fears of a Greek euro zone exit fade.
Cyprus sought financial help last year after its banks suffered huge losses from Greece's sovereign debt restructuring. The island, which has been shut out of international financial markets since May 2011, needs about 17 billion euros in aid - roughly the same as its gross domestic product.