BERLIN, Germany — Greece seems caught between a rock and a hard place, between its private creditors and the EU finance ministers.

The private creditors are insisting they cannot agree to a greater voluntary haircut than the one they have offered, whereas the euro zone is saying that offer is not good enough.

On Wednesday the country’s private creditors were gathering in Paris to take stock, following the rejection of their final offer by the euro zone ministers. The steering committee of the Institute of International Finance (IIF) was meeting to discuss how to advance the stalled talks as time runs out for Greece.

The creditors had agreed to a voluntary loss on Greek sovereign debt that they hold, by swapping the bonds for new ones with lower interest rates, but the IIF has balked at a return of anything less than 4 percent on the new bonds.

The EU finance ministers who met on Monday and Tuesday in Brussels said that this would not be enough to cut Greek debt down from the current 160 percent of GDP to 120 percent by 2020, which is estimated to be the minimum required to get the Greek economy back on its feet. They want an interest rate of around 3.5 percent.

On Wednesday, Athens sought to be upbeat about the progress of talks. Government spokesman Pantelis Kapsis said that the IIF head Charles Dallara was due back in Athens on Wednesday, and that “the target is to conclude the ... agreement even within this week.”

On Tuesday, Greek Finance Minister Evangelos Venizelos said in a statement that the talks were entering the final stretch. “I believe everyone has now realized that Greece must be supported in its effort, which is of vital importance not only for us but for the euro zone as a whole and the global economy.”

The deal with the creditors is required before Greece can access the next euro zone bailout of 130 billion euros ($168 billion), something it needs urgently ahead of March, when 14.5 billion euros worth of bond redemptions come due.

Without a deal, Athens could be forced into a hard default, which could push up the debt of other weak euro zone members. On Tuesday, the Standard & Poor’s rating agency said that it would likely downgrade Greece to “selective default,” whether or not the debt restructuring is achieved.

If the investors decide against agreeing to the EU ministers’ terms, then the euro zone faces a painful choice between a Greek default and providing debt relief on the bailouts.

Christine Lagarde, head of the International Monetary Fund, warned Wednesday: “If the level demanded by the private investors is not reached, then public creditors will have to step in to.”

Yet the EU is worried at Greece’s progress, and wants more commitments on the implementation of reforms and austerity measures.

“Greece has fallen short of its reform and austerity targets by a wide margin,” Austrian Finance Minister Maria Fekter said after the Brussels meeting on Tuesday. She said that the Greeks had been “sent home with a list of things they need to fulfill” before receiving a second bailout.