Banks are making progress in talks to contribute to the rescue package for Greece, the lobby group heading the private sector's efforts said on Sunday.

The Institute of International Finance (IIF) said talks continued in Rome on Thursday and Friday, hosted by Vittorio Grilli, in his capacity as head of the European Union's Economic and Finance Committee.

Progress has been made and the discussions are continuing, the IIF said in a brief statement.

Private investors in Greek bonds are discussing with public sector officials several options related to Greece's financing needs and longer-term debt sustainability. The IIF declined to provide more details on timing or the nature of the talks.

An IIF paper a week ago said euro area member states and the IMF needed to act soon to avoid the risk of contagion accelerating. It wants any rescue to include a programme to buy back Greek bonds to cut the country's debt mountain and provide a sustainable long-term platform.

(Reporting by Steve Slater; Editing by David Hulmes)