"I think we should not use taxpayers' money," Anders Borg told reporters. "The guarantee system alone cannot solve solely the problems. We have to restore credibility with capital."
European leaders are holding a series of meetings to try to resolve Greece's worsening debt crisis and its knock-on effects on the European banking system. No decision is expected at a summit on Sunday and a second summit has been scheduled for Wednesday.
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EU finance ministers are trying to make the European banking system more resilient to the possibility of a default in Greece and any wider contagion across the continent. EU officials say almost 100 billion euros is required to shore up the region's banking system. Banks that cannot raise money on the markets will have to turn to national governments, and finally to the European Financial Stability Facility (EFSF).
European banks will be required to increase their core tier one capital ratio to 9 percent to help them withstand losses on sovereign debt, banking sources have said.
Deep divisions between France and Germany over the best way to scale up the euro zone's bailout facility have prevented agreement on the way forward, but there were signs on Friday that some progress had been made.
German Chancellor Angela Merkel, French President Nicolas Sarkozy and Europe's top two officials, European Council President Herman Van Rompuy and European Commission President Jose Manuel Barroso, will meet late on Saturday to try to break the deadlock before Sunday's summit.
EU leaders will then try on Sunday to agree a comprehensive plan to resolve the two-year-old debt crisis, and will meet again on Wednesday if necessary.
Discussions are expected to include ways to make Greece's debt mountain more manageable. An analysis by the EU and the International Monetary Fund showed on Friday that private holders of Greek debt may need to accept losses of up to 60 percent on their investments in any credible plan.
"It is pretty obvious we need a substantial haircut for Greece," Swedish Finance Minister Borg told reporters on Saturday.
Greece's finance minister welcomed a decision late on Friday by euro zone finance ministers to approve an 8 billion euro loan tranche that Athens needs next month to pay its bills.
"The disbursement of the sixth tranche is an important and productive step," Evangelos Venizelos told reporters on Saturday. "Greece is not the central problem, now the point is to take more general and more constructive decisions for the euro zone as a whole."
(Reporting by Robin Emmott and John O'Donnell; editing by Tim Pearce)