ROME, July 7 - International banks, under pressure from European governments to help with another Greek bailout, discussed buying back the country's bonds in another attempt to stitch together a rescue plan after a French initiative failed.

European Central Bank and Greek government officials as well as international and Italian banking executives met lobby group the Institute of International Finance (IIF) in Rome on Thursday, an Italian Treasury source said. Another source close to the discussions said Deutsche Bank took part.

The banks are struggling to strike a deal which would let private sector creditors provide cash and breathing space to Greek debtors without being defined as a default by credit ratings agencies -- which have warned they are watching closely.

The IIF said the group had discussed debt buy-back approaches, but did not elaborate.

In an emailed statement it said attendees had tried to refine the options that were discussed in the IIF's Board statement of last Friday.

That statement referred to possible debt buyback proposals, which could, along with further Greek fiscal adjustment, begin to reduce and therefore help service the country's debt.

But the banks remain split on how best to construct the aid. Thursday's meeting followed a similar one organized by the IIF in Paris Wednesday at which a menu of options was discussed, according to Charles Dallara, the managing director of the bank lobby group.

A French proposal for a rollover in which bondholders would reinvest at least 70 percent of the proceeds from bonds maturing before the end of 2014 in new 30-year Greek debt has run into ratings agency objections.

Officials are now looking at a broader range of options.

The Treasury source confirmed that the meeting had broken up around midday GMT.

The source said earlier that there would be an exchange of views on developments so far and the solutions currently on the table for the involvement of private creditors.

The meeting was chaired by Vittorio Grilli, director general of the Italian Treasury, in his capacity as chairman of the European Union Economic and Financial Committee.

An EU source also confirmed the meeting in Rome and said EU representatives would be attending. However no representative from any of the ratings agencies was expected to be present.

Following the effective veto on the French plan by ratings agency Standard and Poor's, which said it would consider the operation contained in the proposal as a selective default, the search has widened for an alternative plan.

Germany has raised other possibilities including getting banks holding Greek bonds to swap them for new bonds with longer maturities but that proposal has not found favor with banks and some other European governments.

German Deputy Finance Minister Joerg Asmussen said the idea of a bond exchange could be put back on the table, with talks likely to take place over the summer.

Thursday, Dutch Finance Minister Jan Kees de Jager was quoted by the daily Het Financieele Dagblad as saying that private sector banks must be pressured into taking part in a bailout as a voluntary deal was not realistic.

(Additional reporting by Francesca Landini in Milan and Edward Taylor in Frankfurt; writing by James Mackenzie; editing by Sophie Walker)