Germany has warned that private creditors will need to roll over the Greek debt if Berlin is to agree a new bailout running to tens of billions of euros in the next fortnight.

The ultimatum from Wolfgang Schäuble, the German finance minister, put Berlin on a collision course with Paris, Frankfurt and Brussels, where the French government, the European Central Bank, and the European commission oppose a restructuring of Greek debt.

In a letter to the ECB, the commission, and the other 16 finance ministers of the eurozone, Schäuble for the first time conceded the need for a new Greek bailout, in effect admitting that the €110bn (£98bn) rescue agreed last May had failed. He warned that the eurozone could be confronted with its first sovereign debt default within weeks if agreement was not reached on a new Greek rescue.

"Without another disbursement of funds before mid-July, we face the real risk of the first unorderly default within the eurozone," Schäuble wrote in the letter obtained by the Guardian. "Any additional financial support for Greece has to involve a fair burden-sharing between taxpayers and private investors."

Germany has long invoked the principle of moral hazard in structuring the eurozone bailouts of the past year, arguing that creditors should not reap profits on the bond markets while leaving the public purse and European taxpayers to fund the rescues. The argument has provoked strong resistance from the European commission, which has warned that forcing the international banks and other private creditors to take "haircuts" or large losses on their lending to governments would spell disaster. Jean-Claude Trichet, the president of the ECB, is a loud critic of the German position, arguing it could trigger a renewed crisis.

But the government of the chancellor, Angela Merkel, the central player in the effort to prevent a Greek meltdown over the next month, is caught between intense international pressure to act and domestic resistance to throwing more German taxpayers' money at profligate eurozone countries.

In Washington this week US president Barack Obama told Merkel that the euro crisis could spell disaster for the US economy and urged her to lead the effort to prevent an "uncontrolled spiral of default …America's economic growth depends on a sensible resolution of this issue."

But in Berlin Merkel and Schäuble faced stiff resistance in parliament to a new Greek bailout. By forcing the banks and other creditors to bear some of the pain, the Merkel government hopes to win over reluctant MPs and the German public.

Figures circulating in Brussels suggest that a new Greek bailout will need to amount to about €60bn, with expectations that this could soar to €100bn by 2013 when a new permanent eurozone bailout fund is established.

According to reports in Germany, Schäuble's officials reckon that €30bn could be shaved off if the banks reached agreement with the Greek government on bond swaps, in effect rolling over the debt for a period of seven years.

Schäuble's letter, dated Monday, was the first time the government in Berlin had formally acknowledged the need for another bailout. In line with German practice over the past year of crisis, it then sought to dictate the terms.

In a dig at Trichet, Schäuble said that any agreement between the Greek government and its private creditors would need to go "beyond a pure Vienna initiative approach", referring to a "soft" and "voluntary" rescheduling by the banks. There needed to be a "quantified and substantial contribution of bondholders to the support effort".

Behind the letter lies a more detailed blueprint drawn up by the German finance ministry that would penalise those creditors who refuse to take part and reward banks that agree to roll over the debt by conferring priority on their claims when the bonds mature.

According to new figures from the Bank of International Settlements in Basle, international banks have fled the Greek bond market over the past year, with the notable exception of the Germans, by far Greece's biggest foreign private creditors.

By the end of last year, non-Greek European banks had cut their lending to Greece by a third to $52.3bn (£31.9bn) of the $280bn Greece owes in bonds. But German exposure was only very slightly down at $22.7bn, indicating that the German banks had accepted government urging to keep credit lines open to Athens.