Talks to resolve the Greek debt crisis continued Thursday amid ongoing disagreements among private creditors, the European Central Bank and other parties about which degree of losses might be considered acceptable and who might have to be included in those losses.

Christine Lagarde, head of the International Monetary Fund, further roiled the waters by suggesting that the ECB and other public bodies might have to accept losses as well, something the ECB has refused to consider.

Bloomberg reported that after Lagarde made her suggestion, Michael Meister, deputy floor leader for German Chancellor Angela Merkel’s Christian Democrats and the party’s ranking finance spokesman, dismissed the idea out of hand that the ECB should even consider taking losses on Greek debt. In the report he was quoted saying, “I can’t imagine that European politicians would allow third parties to make such an indecent claim on our central bank.”

So far, negotiators for private bondholders, led by Charles Dallara and Jean Lemierre, of the Washington-based Institute of International Finance, have been holding out for a higher interest rate on coupons for new bonds to be exchanged for ones presently held by Greece’s creditors.

Dallara has also suggested that all parties holding Greek debt be prepared to accept haircuts so that the arrangement is fair. The ECB has refused to consider such a measure, saying that it would jeopardize faith in the institution. Dallara pointed out on Wednesday that private creditors hold approximately 60% of Greek debt, with the rest in the hands of public institutions and other governments.

Hedge funds have also been contributing to the suspense over the discussions, with some resolved to hold out for full repayment or else a triggering of credit default swaps to achieve payment. That would result in a default for Greece and could possibly throw the entire eurozone into turmoil.