Greece and its creditors are continuing negotiations on a debt swap on Saturday after late-night talks edged them closer to a vital deal but failed to clinch an agreement.

Athens is anxious to strike a deal before a meeting on Monday of euro zone finance ministers, just in time to set in motion the paperwork and approvals necessary to receive a new injection of aid to avoid a messy bankruptcy in March.

The elements of an unprecedented voluntary PSI are coming into place, the Institute of International Finance said in a statement after Friday's three-hour evening negotiation session, referring to the bond swap scheme.

Now is the time to act decisively and seize the opportunity to finalize 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.

IIF chief Charles Dallara, who negotiates in the name of the private bondholders, will resume talks with senior Greek officials on Saturday. No time was set yet for the meeting.

We will not know anything for sure before Monday, said a banking source close to the talks. 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.

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.

It will be near cash-equivalent short-term EFSF bonds, one of the sources said.

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.

The two sides are still discussing the coupon and some technical details, a Greek banker close to the talks said on Saturday. After Friday's meeting, we are in a better position and closer to a deal, but I don't think we should expect any announcement today.

ECB'S ROLE

Another source close to the talks said the European Central Bank's part in the deal was also discussed.

We expect them to make an effort as well. It could be through a special deal, as you would expect for a body like the ECB, the source said.

Greece needs to have a deal in the bag before funds are doled out from a 130 billion euro rescue plan that the country's official lenders, the European Union and the International Monetary Fund, drew up in October.

The IMF insists that the debt swap deal must cut Greece's debt burden enough to bring it down to 120 percent of GDP by 2020 from 160 percent now, as agreed in October, which is made even more difficult by the fact that Athens' economic prospects have deteriorated since.

Senior EU, ECB and IMF officials from the troika of foreign lenders began meetings with the government on Friday to discuss reforms and plans to finalize that bailout package.

The deal must be completed. There is no more time left, said a Greek government official who requested anonymity.

The paperwork alone is expected to take weeks, meaning failure to secure a deal soon could put Athens at risk of a chaotic default in March, which in turn could jolt the financial system and tip the global economy into recession.

(Writing by Deepa Babington and Ingrid Melander; Editing by Andrew Heavens and Alison Birrane)