BRUSSELS — Confronting the looming prospect of a second bailout for Greece, European finance ministers insisted Tuesday on further deficit-cutting efforts from the government in Athens and acknowledged for the first time that the private sector could be included in a restructuring of Greek loans.

Two days of talks in Brussels ended with public concessions that the idea of “reprofiling” Greek debt, or voluntarily extending maturities without changing interest rates or the amount of the loan, was being contemplated, at least as a last resort.

For months, European officials have been wary of any discussion of private sector involvement in the restructuring of Greek loans before 2013, fearing a negative reaction in the markets.

That taboo was broken by Jean-Claude Juncker of Luxembourg, who presides over the euro zone finance ministers’ meetings, when he said late Monday that he would not exclude “a kind of reprofiling.” Mr. Juncker then referred Tuesday to a “soft restructuring of Greek debt.”

The suggestion was refined by the deputy finance minister of Germany, Jörg Asmussen, who said Tuesday that it might be considered as a last resort.

If other moves prove insufficient, “we’ll have to consider measures that aren’t just at taxpayers’ expense but also involve the private sector on a voluntary basis,” Mr. Asmussen said.

The policy shift follows intensive talks in which several ministers expressed frustration at the meager progress Greece has made so far on a promised program of state asset sales to investors that would raise 50 billion euros ($71 billion) .

Within a fractious monetary union, the politics of offering new loans are increasingly difficult, particularly if voters in creditor countries do not see greater evidence of Greek consolidation.

“They promised 50 billion of privatization, but they are still where we were in the 1970s,” said Maria Fekter, the Austrian finance minister, referring to Greece.

But with its debt level now at almost 150 percent of gross domestic product, Greece risks being trapped in a spiral of negative growth, prompting speculation that a new package of about 30 billion euros of new loans may be needed.

Officials from the European Central Bank, the International Monetary Fund and the European Commission, the executive arm of the European Union, are compiling a report to be used next month when the governments contemplate a second bailout — nicknamed “Grease II.”

But before agreeing to a second round of aid, finance ministers want more evidence that Greece is fulfilling its part of the existing bargain.

Olli Rehn, the European commissioner for economic and monetary affairs, said that although Athens had made budgetary adjustments in the last 12 months, further “decisive steps by the Greek authorities are indispensable.”

The Dutch finance minister, Jan Kees De Jager, said, “We now expect Greece to do the heavy lifting by cutting, reforming and privatizing, painful as it is.” He added, “If Greece doesn’t deliver on its promises and the I.M.F decides not to extend the second tranche of its loans, the Netherlands will follow the I.M.F.”

The depth of division over the rescue plans was highlighted Tuesday by Michael Noonan, the Irish finance minister, who suggested that the terms attached to European bailouts were so stringent that they threatened to make growth impossible and were thereby self-defeating.

“You can enhance the possibility of success of the programs if you reduce the pricing,” said Mr. Noonan, who is campaigning for a reduction in the interest paid on Ireland’s bailout loans.

Mr. Noonan said that the mindset under which struggling countries were asked for concessions in exchange for easier conditions “was not the smartest way to proceed.”

Ireland’s bid for lower rates has run into resistance from France and Germany, which want an increase in the low Irish corporate tax rate of 12.5 percent. But Mr. Noonan ruled out any such concession.

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