So-called non-performing exposures (NPEs) are the biggest challenge facing the sector. At the end of June they had fallen by 4.1 percent from the first quarter to 88.6 billion euros (79.7 billion pounds) or 47.6 percent of banks' overall loan book compared with a target of 90.2 billion euros or 46.9 percent.

Greek banks have been under regulatory pressure to tackle the bad debt problem which restricts their ability to expand credit and help the economy's recovery.

The country's debt crisis since 2010 drove unemployment to nearly 28 percent, which stopped many borrowers from servicing their loans and shrank the economy by a quarter.

European Central bank board member Benoit Coeure said earlier this week that reducing the burden of sour debt should be a top policy priority for Greece's banking sector.

"Reducing NPLs (non-performing loans) is certainly top of the list from our point of view. Only stronger and healthier banks can provide the necessary basis for an increase in the supply of credit that can support economic growth," he told Greek newspaper Kathimerini.

NPEs comprise restructured loans likely to turn sour and non-performing loans (NPLs), which are credit past due for more than 90 days. Cutting them would free up more capital to fund productive sectors of the economy.

Greek lenders had NPEs totalling 14.5 billion euros ($16.3 billion), or 5.5 percent of loans, when the global financial crisis began in 2008.

While NPEs soared to 106.9 billion or 50.5 percent of loans at the end of June 2016, banks have agreed with ECB regulators to shrink them to 64.6 billion by end-2019, meaning the NPE ratio will fall to 35.2 percent of their books.

The agreed targets are back-loaded, meaning most of the reduction will take place this year and in 2019. Banks are aiming for a 37 percent reduction by December next year.

The reduction in the second quarter was brought about mainly by loan sales of nearly 2.0 billion euros and write-offs of 1.6 billion.

The second quarter also saw collections and liquidations. Default rates picked up to 2.1 percent and were higher than the pace of restoring loans back to performing status (cure rate) of 1.8 percent, the central bank said.

At the end of June, the NPE ratio of mortgages was 44.3 percent, that of consumer loans 56.9 percent with sour business loans at 48 percent. Coverage by loan-loss provisions was 48.6 percent, slightly down from the first quarter's 49 percent.

Greece's four major banks - Piraeus, National, Eurobank and Alpha - and three less systemic banks submit data on nine operational targets.

(Reporting by George Georgiopoulos; Editing by Elaine Hardcastle)

By George Georgiopoulos