On Monday, euro zone finance ministers rejected an offer made by private bondholders to help restructure Greece's debts terming it as insufficient to send back negotiators to the drawing board and raising the threat of Greek default.

The EU ministers said they could not accept demands of the bondholders for a coupon of four percent on new, longer-dated bonds that are expected be issued in exchange for their existing Greek holdings.

A 4.0 percent coupon is the least they can accept if they are going to write down the nominal value of the debt they hold by 50 percent, said banks and other private institutions represented by the Institute of International Finance (IIF).

"Ministers asked their Greek colleagues to pursue negotiations to bring the interest rates on the new bonds to below 4 percent for the total period, which implies the interest comes down to well below 3.5 percent before 2020," Jean-Claude Juncker, the chairman of the Eurogroup countries, said.

Olli Rehn, the European commissioner in charge of economic and monetary affairs, said he expected a deal on PSI to be struck "within days," despite the disagreement.

A report by The Financial Times that German Chancellor Angela Merkel was ready to see the ceiling of the combined firewall raised to 750 billion euros in exchange for agreement on tighter euro zone budget rules was immediately denied by her chief spokesman, Steffen Seibert.