German officials are demanding that private investors contribute a “substantial” amount toward any new bailout of Greece and warned that the country faces an “unorderly default” within weeks if an agreement is not reached.

The demand, conveyed to European and International Monetary Fund officials in a letter this week from German finance minister Wolfgang Schauble, came as negotiations over Greece reach a do-or-die stage.

Amid a renewed sense of crisis, IMF and European officials are discussing how to revise and expand aid to Greece. They hope to complete a new program at summit meetings beginning June 20. The country may need more than $100 billion for a new three-year program, including roughly $40 billion to pay bonds coming due in the next year and a half.

The process is being closely monitored in the United States, where President Obama warned this week of “disastrous” results if Greece defaults on payments to its bondholders.

In Athens, Greece’s elected leaders are trying to push a fresh package of budget cuts through Parliament as street protests mount and the latest economic data reflect a worsening situation. Unemployment in February topped 16 percent, Greece’s statistics agency reported Wednesday, more than the IMF had projected.

The IMF and European officials provided a round of emergency lending to Greece last year on the condition that it make cuts to its public pensions and other social spending, reduce the size of the public payroll, privatize state-owned industries and take other steps to curb public borrowing. The country’s debt now far exceeds the government’s ability to pay.

While the IMF considers the steps vital for restoring Greece’s long-term growth, the austerity measures have sapped the economy more than expected — leaving Greece deeper in debt and with slower growth than the IMF anticipated.

Schauble’s demand that investors help pay for the Greek bailout reflects German politics. German officials face their own discord at home and are pushing for what Schauble termed a “quantified and substantial contribution” from private bondholders that would reduce the amount Greece needs from the IMF and other European countries and lessen the sense that Europe’s more successful nations were underwriting others.

He suggested that existing bondholders be made to wait an additional seven years for full repayment — continuing to collect interest in the meantime but decreasing by tens of billions of dollars the amount Greece would need to pay out in the intervening years.

The risks are high. Credit ratings agencies have said a forced extension of existing bonds would be considered a default, undermining the financial health of German, French and other banks that hold Greek bonds, possibly damaging the ability of other European nations to borrow and probably prompting a new financial crisis in Greece.

While debate has focused around a “voluntary” program that bondholders could accept or reject, structuring such an effort may prove difficult.

“The point is whether you can find conditions under which bondholders would be willing to exchange that debt for something with a longer maturity without their being coercion,” said Jens Larsen, chief European economist with RBC Capital Markets. “If you do it by saying, ‘Take these bonds’ and make the old stock unusable, then that may sound clever but it is almost certainly perceived as coercion.”

The Greek predicament has become entangled in the debate over who should become the new head of the IMF, replacing Dominique Strauss-Kahn.

One of the main figures in the European negotiations over Greece is French finance minister Christine Lagarde, who is also campaigning for the IMF job. The post would give her even greater power to help Europe. French officials, partly out of concern for their country’s banks, have been prominent among those who object to forcing private bondholders to aid Greece.

Lagarde’s main opponent for the IMF job is Mexican central bank governor Agustin Carstens, who helped negotiate a debt restructuring for his country in the late 1980s. He has said he regrets that it was not done years earlier to get the Mexican economy growing again.

The IMF wants to avoid involving private creditors in a Greek bailout. The agency’s chief representative in Athens this week called the idea “very dangerous” and something “that we really do not know whether we will be able to control.”

The IMF has supported debt restructuring in other cases — such as Uruguay in 2003, when the country’s creditors agreed to extend the length of their loans to ease the amount Uruguay had to pay out each year.

Some analysts suggest that European nations have rushed to back Lagarde for IMF chief because they consider her more sympathetic in addressing the continent’s public debt problems. Carstens has argued that “fresh eyes” might help address Europe’s problems more quickly.