The IMF's previous calls for an asset quality review had sparked fears of another dilutive capital injection for banks' shareholders, hammering the sector with steep losses of more than 30 percent since mid-August.

"On the subject of the Greek banking system, let me emphasise that we see no financial stability concerns at all in Greece," Poul Thomsen, head of the IMF's European Department, said in a statement.

"The issue is that we need to be sure that there is a strategy to deal with Greece's exceptionally high level of non-performing loans over the medium term."

Thomsen's statement followed hints by Greece's finance minister on Wednesday that the fund would drop its demand for an asset quality review (AQR), echoing comments by an IMF spokesman in Washington.

Greek banks have been recapitalised three times since the debt crisis exploded in 2010 but are still burdened by 100-plus billion euros of soured debt. They have committed to targets to reduce the load to 66 billion euros (58.12 billion pounds)by 2019.

"It's a relief rally on the back of what appears to be a clearing of a blurry backdrop," said Eurobank Securities analyst Nick Koskoletos.

Greece's four big banks - Piraeus (>> Piraeus Bank SA), National (>> National Bank of Greece), Eurobank (>> Eurobank Ergasias SA) and Alpha (>> Alpha Bank SA) - will be part of pan-European stress tests next year by the European Central Bank.

The Athens bourse's banking index <.FTATBNK> was up 10.3 percent, adding to early trading gains, on what traders said was relief that a compromise was reached on the issue.

The ECB has offered to bring forward its stress test of the Greek banks, finalising data before Greece exits its three-year, 86-billion-euro international bailout in August.

After two years of wrangling over debt relief, the IMF agreed to support conditional participation in June as part of a deal that unlocked 8.5 billion euros in loans

The ECB, which supervises top Greek banks, has firmly rejected the IMF's push for a fresh asset quality check.

Thomsen said the ECB's proposal to bring forward its planned pan-European bank health test and undertake targeted asset reviews was constructive.

It would allow the fund to assess whether the current strategy to ensure the soundness of the Greek banking system is adequate "without having to go through a full asset quality review (AQR)."

"We think it is a constructive proposal that achieves the same broad objectives, and we are now discussing the exact modalities with our colleagues at the ECB," Thomsen said.

The Bank of Greece, the central bank, has in the past disputed the IMF's view that Greek banks may need a 10 billion-euro capital buffer because of remaining risks to their asset quality.

(Reporting by George Georgiopoulos, additional reporting by Renee Maltezou,; Editing by Edmund Blair/Keith Weir)

By George Georgiopoulos