BERLIN—The International Monetary Fund is demanding that Europe free Greece from all payments on its bailout loans until 2040, in the opening bid of a struggle that pits IMF math against German muscle.

A new IMF proposal shared with Europe late last week goes far beyond what Greece’s eurozone creditors, led by Germany, have said they are willing to do to help the country regain its financial health. Germany is leading the pressure on the IMF to dilute its demands and rejoin the Greek bailout program as a lender.

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