International bankers and European Union officials made no progress in securing a private sector contribution for a second bailout of Greece and bond yields climbed on concern about the scheme.

The managing director of the Institute of International Finance (IIF), a group representing around 400 banks and financial organisations, met representatives from the European Central Bank, the Greek government and the euro zone in Rome to try to break a deadlock over how private creditors might voluntarily maintain their exposure to Greek sovereign debt.

It was the latest in a series of meetings in recent weeks, but there is little sign of the parties reaching a deal.

Yesterday's meeting, which explored a possible buyback of Greek debt, broke up with no conclusion. To avoid a debt default by Greece, euro zone finance ministers are trying to put together a second international bailout by mid-September.

A private sector debt rollover, in which investors would buy new Greek bonds as existing ones matured, is an important part of the new rescue plan.

Until yesterday, efforts had focused on a French proposal to roll over up to 70 per cent of Greek debt maturing before the end of 2014, with a portion of that going into new 30-year Greek bonds that would be guaranteed by other AAA securities.

But attention has now shifted to the possibility of buying back Greek debt, or switching existing Greek bonds for longer-dated ones, which could trigger a default.

In a statement, the IIF said participants had discussed 'debt buy-back approaches', but did not go into details.