"To bring the debt ratio down further, one needs to take recourse to measures that would entail capital losses or budgetary implications for euro area member states," the document says.
"Capital losses do not appear to be politically feasible and would jeopardise, at least in a number of member states, the political and public support for providing financial assistance."
Juncker said at a meeting a week ago that he wanted to extend the target date to reduce Greek debt by two years to 2022, but Lagarde insists the 2020 goal should stand.
The view of the IMF, which has played a role in both Greek bailouts so far, is critical since it provides international legitimacy and credibility for the efforts the euro zone is making. If the IMF were to withdraw its support for the bailout programmes, it could have a deeply damaging market impact.
The document appeared designed in part to convince the IMF that Greek debt could be made sustainable just two years behind schedule if only it would soften its stance.
It remains possible that Lagarde could provide further wiggle room, but she is believed to favour the idea of euro zone member states taking a writedown on some of the loans extended to Greece in order to stick to the 120 percent in 2020 goal.
Among the main measures under consideration to bring Greece's debt burden down as rapidly as possible is a debt buy-back under which Greece would offer to purchase bonds from private investors at a discount to their nominal value.
Several options are under consideration, officials have said and the document makes clear, including using about 10 billion euros to buy back bonds at between 30 and 35 cents in the euro.
There are also proposals to reduce the interest rate on loans already extended by euro zone countries to Greece, to impose a moratorium on interest payments and lengthen the maturities on loans, all of which would cut the debt burden.
Pressure for the euro zone to come up with a solution is high not just because Greece is running out of money and financial markets want a dependable