A new front has opened whether to provide permanent relief for Greece's $330 billion debt, whether by extending repayment, encouraging creditors to take a loss, called taking a haircut, or canceling some of what's owed outright.

　　The International Monetary Fund, one of Greece's many creditors, says that, without some form of debt restructuring, the Greek economy will remain in freefall.

　　Earlier today, I talked about that with the IMF's managing director, Christine Lagarde.

　　Christine Lagarde, thank you so much for joining us.

　　CHRISTINE LAGARDE, Managing Director, International Monetary Fund: Pleasure.

　　GWEN IFILL: After everything we have seen develop in Greece over the last several weeks and especially in the last week, you have said that even more might be necessary, that debt relief is important. How would that happen?

　　CHRISTINE LAGARDE: It can take different forms.

　　It could be significant rescheduling, with extension of maturities over time, with an extended grace period, with compressed interest. It can be a haircut. It can be budget transfers. I think on the — I'm very realistic, and we try to be. What we heard loud and clear is that the euro area members are not particularly keen to do haircuts. That was clear. And budget transfers is not in the cards either.

　　GWEN IFILL: So writing off part of the debt is not an option?

　　CHRISTINE LAGARDE: It's — I think what we said is significant restructuring, which can take the form of a reprofiling for Greece.

　　GWEN IFILL: Is that something that your European partners are fans of?

　　CHRISTINE LAGARDE: I don't think any creditor is a fan of any kind of reprofiling, because what it means is that you carry the debt in your books for much longer and you carry the claim in your books for much longer.

　　So, no, no creditor is keen to do that. But it's also important to actually make sure that the country is on track, that the debt is sustainable, and that there is a chance of reimbursement.

　　GWEN IFILL: Was it also because of the political ramifications that we didn't hear about this earlier, that you didn't push harder for this as part of the original negotiations?

　　CHRISTINE LAGARDE: Oh, it's been on the table of negotiations all along.

　　And the IMF has been very clear all along that the debt issue was to be addressed and was critical. That's not a — it's not a new development. It's been probably more public on the basis of transparency, because I think it's just best to have it all out. But it's been very clear to all the euro area finance ministers, to the euro area partners, to everybody.

　　GWEN IFILL: The question is a matter of magnitude, really, how much trouble Greece is in, how much more serious it is than even it seemed to be a week ago.

　　CHRISTINE LAGARDE: You're right. It's a matter of amount, how much of it has to be reprofiled, so that Greece looks at the sustainable parts, and we believe that it's a significant amount.

　　GWEN IFILL: Prime Minister Alexis Tsipras has not been, how shall we say, enthusiastic about this deal, even though he agreed to it and continues to push for it, but very reluctantly. Would you like to see him push for it harder?

　　CHRISTINE LAGARDE: There are two ways to look at it.

　　You look at the votes last night, and it's quite an impressive vote to support the proposal and to actually take the steps, which is even more encouraging, in terms of development. And then there is the ownership of it all.

　　I think ownership, and I hope ownership is going to come gradually, as those measures will actually unfold in a satisfactory manner, will unleash additional financing, will help the country towards being more stable, people having better access to their own finances.

　　GWEN IFILL: I wonder if it requires public opinion to shift away from where it is right now, and what we have seen in the past and which caused such heartburn this time was that Greece has not lived up to its pledges and commitments, or at least a lot of European leaders feel that. What's different this time?

　　CHRISTINE LAGARDE: There are two things.

　　One is, there is a very strong aspiration by the Greek people to be part of the euro area, to stay within the zone, to keep that currency, and that's a positive. The second thing is that to actually be a member of the club, you have to play by the rules.

　　And if we see the momentum observed in the last few days since the weekend, however difficult it has been, however laborious, if we see that momentum continue and pick up with very difficult negotiations coming up and difficult implementation to follow, then it means that not only are they enthusiastic about being in the Eurozone, but they're also prepared to take the right measures to free up the economy, to privatize what needs to be privatized, to respect the budget rules that need to be respected and to unleash the potential of the Greek economy.

　　GWEN IFILL: Let's talk about being a member of the club. The German foreign — finance minister today raised the specter again of Greek exiting the euro, something which I thought had been settled. Is this still a live possibility, do you think?

　　CHRISTINE LAGARDE: It's a point that was in the initial draft on Saturday night or Sunday morning, which has been moved out of the final euro area communique signed off by the leaders.

　　GWEN IFILL: A temporary exit and then coming back?

　　CHRISTINE LAGARDE: Yes, that was taken out of the draft.

　　So the document that is the law of the parties now is that communique, which does not include the temporary exit. Of course, everything else needs to be done, so balanced program, commitments on the parts of the Greek to reform the economy, to move towards safe, healthy fiscal policies, and, on the other hand, support by the euro area partners in terms of both financing, because they need additional financing soon, and debt restructuring, in order to lighten the burden of debt going forward.

　　GWEN IFILL: And I guess the question is, is there willingness? Is there willingness?

　　CHRISTINE LAGARDE: I know how hard it is going to be, no question.

　　But I'm encouraged by what has happened over the last four days. Strong, you know, momentum laboriously built over the weekend. And then I said — yesterday, I said very tight timetable, colossal challenge. I think the very tight timetable, they're delivering against. They passed the legislation yesterday.

　　The ECB took notice of it and moved up…

　　GWEN IFILL: The European Central Bank.

　　CHRISTINE LAGARDE: Yes, the European Central Bank moved up the emergency liquidity assistance line.

　　Sooner or later, the banks will reopen, as, you know, a sign that confidence is restored. And the Europeans have found bridge financing in order to pay the outstanding.

　　GWEN IFILL: Christine Lagarde, head of the IMF, thank you very much.

　　CHRISTINE LAGARDE: Thank you so much.