It was the first time Papademos publicly confronted his people with the risk, already mooted by wary EU, IMF and German officials, that the austerity program might fall through if they don't try hard enough.
His remarks were seen as an encouragement to support pro-bailout parties in a snap election expected on May 6.
"Greece will do everything possible to make a third adjustment program unnecessary," Papademos told Italian business daily Il Sole 24 Ore, according to a transcript of his remarks. "Having said that, markets may not be accessible by Greece even if it has implemented fully all measures agreed on.
"It cannot be excluded that some financial support may be necessary, but we must try hard to avoid such an outcome."
Greece secured a 130 billion euro bailout from the International Monetary Fund and the European Union last month after it won agreement from private sector creditors to take part in the biggest debt restructuring in history.
But with its economy in the fifth year of deep recession, skepticism about the effectiveness of government reform measures and deep public resistance to further doses of austerity, there have been widespread expectations that more aid will be needed.
According to an analysis from the IMF, the EU and European Central Bank, even if Greece sticks to its agreed reform program to 2030, it may need more support after 2014.
However, Papademos repeated that Greece would do everything necessary to remain in the euro zone, saying the consequences of an exit would be "devastating".
"More than 70 percent of the Greek people support the country's continuing participation in the euro area," he told the Italian business newspaper. "They realize, despite the sacrifices made, that the long-term benefits from remaining in the euro zone outweigh the short-term costs."
Speaking in parliament on Friday, Papademos warned lawmakers that the government would need to identify almost 12 billion euros of fresh budget cuts for 2013 and 2014 immediately after the upcoming election, expected on May 6.
"What's important is to implement the policies included in the (bailout) program in an effectively and timely manner," he said. "If this doesn't happen, nobody can expect its anticipated results to materialize."
(Reporting by Stephen Jewkes and Harry Papachristou in Athens; Editing by Mark Heinrich)
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