The representatives of Greece's private creditors left Athens unexpectedly on Saturday without a deal on a debt swap plan that is vital to avert a disorderly default, sources close to the negotiations told Reuters.

Negotiations will continue over the phone during the weekend but it is unlikely that an agreement can be clinched before next week, the sources said, as Athens races against the clock to strike a deal.

A lot of progress has been made on the details of the plan during talks between Athens and Institute of International Finance chief Charles Dallara, sources say, but any deal needs the approval of the IMF and euro zone countries, who insist on a substantial cut in the debt load.

The IMF and EU countries, and in particular the bloc's paymaster Germany, want to make sure the deal puts Greece's derailed finances back on a sustainable track before they agree to a new, 130-billion euro bailout, which is also crucial to avoid a messy default.

The IMF insists the debt swap deal must ensure Greece's debt burden will be cut to 120 percent of GDP by 2020 from 160 percent now, as agreed at an EU summit in October, and has warned that this is made more difficult by the fact that Athens' economic prospects have deteriorated since.

Things are complicated, we are getting closer on the numbers but there is still quite some work ahead, one source close to the talks said. Discussions will continue over the phone this weekend but an agreement is unlikely before next week, if there is an agreement at all.

A meeting Monday of euro zone finance ministers will be crucial for the debt swap talks.

We will want to test the waters among member states because given the complex connections between private sector and official funding elements, we have to have the backing of member states for a deal, a senior EU source told Reuters.

The outcome in terms of achieving the debt-to-GDP target will depend on how the debt sustainability analysis is constructed, which is not a precise science but at most a form of art, the source said.

A new analysis of Greece's debt sustainability could be ready before Monday's Eurogroup, or by mid-week, the source said.

The IIF said on Friday that the elements of the deal were coming into place, adding: Now is the time to act decisively and seize the opportunity to finalise this historic deal and contribute to the economic stability of Greece, the euro area and the world economy.

The statement seemed to be addressing Greece's official lenders, the EU and the IMF, who have driven a hard bargain behind the scenes of the negotiations, insisting that the deal must slash Greece's debt substantially, sources in Athens said.

The euro zone ministers will examine the proposal and say whether we have a deal. If they say we don't, we're back to the negotiating table, said a banking source close to the talks.

Private bondholders will likely take a hit of 65 to 70 percent on their holdings, with Greece's new bonds featuring 30-year maturity and a progressive coupon, or interest rate, averaging out at 4 percent, another banking official close to the talks told Reuters.

A 15 percent cash sweetener will be made up of short-term bonds from Europe's temporary bailout fund, the European Financial Stability Facility (EFSF), two sources told Reuters.

Haggling over the coupon had held up the long-running talks as Greece raced to wrap up an agreement, raising the prospect of a messy default when Athens faces 14.5 billion euros ($18.5 billion) of bond repayments in March..

(Additional reporting by Paul Taylor in Paris and Lefteris Papadimas in Athens; Writing by Ingrid Melander; Editing by Alison Birrane)