The ECB and European central banks have so far been exempt from a cut in the value of their Greek debt portfolios, estimated at more than €50 billion ($65 billion), to the annoyance of private bondholders who face an overall loss of about 70 percent.

The agreement, Venizelos said, must be struck by Monday, when finance ministers from the 17 countries using the euro meet in Brussels — although the date could be “slightly adjusted.”

“One of the major outstanding issues that must be solved … is to secure the terms of participation of the official sector, that is our European partners and the IMF … in the effort to reduce the Greek public debt,” Venizelos said.

Venizelos told a meeting of Socialist party deputies that Greece’s target of reducing its crushing debt to sustainable levels by 2020 “requires the completion of a parallel Official Sector Involvement” — beyond the €100 billion writedown all but concluded with private bondholders.

He added: “That means that the European Central Bank must be mobilized, that we must solve issues concerning national central banks, and we must resolve issues concerning the level of the interest rate” of the first, €110 billion ($144 billion) bailout that has been shielding Greece from bankruptcy for the past 20 months.

A European Union official said Greece needs about an extra €15 billion ($20 billion) to get its debt down to manageable levels, and the rest of the eurozone could have to make up the shortfall. The official spoke on condition of anonymity because of the sensitivity of the matter.

German Finance Minister Wolfgang Schaeuble said on n-tv television Thursday that he didn’t see the need for “any extra contributions from the public sector; we’re carrying everything anyway.” He didn’t address the issue of the €15 billion funding gap.

Athens is locked in tough talks on two fronts to ensure that it remains solvent, dodging the very real threat of a disorderly default — which could likely be followed by a Greek exit from the eurozone — when a big bond issue matures late next month.

On the one hand are the negotiations with banks, pension funds, hedge funds and other owners of devalued Greek government bonds, known as Private Sector Involvement. But the country’s coalition government also has to placate its European partners and the IMF that are urging deeper austerity cuts to release rescue loans from a second package agreed last year — but not yet finalized.

“There were ups and downs in the PSI talks because we, in reality, we’ve been forced to take part in a double negotiation,” Venizelos said.