Greece and its private bondholders inched closer on Thursday to a vital debt swap deal needed to avoid a messy default by Athens, with both sides saying progress has been made and negotiations would continue on Friday.

Nearly a week after talks hit an impasse over the coupon, or interest payment, that Greece must offer on its new bonds under the swap, there were signs the two sides were moving to overcome their differences as time to strike a deal runs out quickly.

The atmosphere was good, progress was made and we will continue tomorrow afternoon, Finance Minister Evangelos Venizelos said after talks with Charles Dallara, head of the Institute of International Finance representing bondholders.

The IIF issued a statement echoing the minister.

Bankers and sources close to the talks say a deal could be wrapped up in the next few days, though previous predictions of a quick resolution have proven premature.

The stakes could not be higher this time. Greece must thrash out a deal within days to pave the way for a new infusion of aid that allows it to avoid bankruptcy when 14.5 billion euros (11.9 billion pounds) of bond redemptions fall due in March.

Even if a deal is struck rapidly, the paperwork will take weeks and Greece's official lenders, the European Union and the International Monetary Fund, say the work must be cleared before funds are doled out from a 130 billion euro rescue plan they drew up in October.

Turning up the pressure before Thursday's round of talks, Venizelos told lawmakers that a large chunk of the bond swap must be agreed by noon on Friday and formalized before Monday's meeting of euro zone finance ministers.

Kept afloat by bailout loans, Greece faces the threat of having to leave the euro zone and slumping into further economic and social misery if it fails to come to grips with its debt, including securing the deal with the private bond holders.

Now is the crucial moment in the final battle for the debt swap and the crucial moment in the final and definitive battle for the new bailout, Venizelos told parliament. Now, now! Now is the time to negotiate for the sake of the country.

Progress had been hard to come by in the latest round of discussions, with bankers worried about being hit by losses far higher than the 50 percent writedown they were expected to take on the nominal value of their bonds.

A source close to the talks said earlier that Athens and its foreign lenders had offered a coupon of just over 3.5 percent during a two-hour meeting on Wednesday, but bondholders rejected that as too low. They were angling for a coupon of at least 4 percent, the source said.

One banker briefed on the talks said progress was made on minor points related to the structure of the deal and the law it would fall under, but the coupon remained a sticking point.

The two sides were roughly one percentage point apart in their demands on the coupon as talks restarted on Thursday.

(Additional reporting by Lefteris Papadimas and George Georgiopoulos; Writing by Deepa Babington; editing by Ron Askew and David Stamp)