* Greece says doesn't need more aid until mid-Nov
* Athens to miss deficit target, economy to shrink
* Admission casts doubt on second bailout plan
* Bank shares slump on fears of bigger writedowns
* Euro zone ministers discuss leveraging rescue fund (Updates after finance ministers' meeting, adds quotes)
By Jan Strupczewski and Harry Papachristou
LUXEMBOURG/ATHENS, Oct 3 (Reuters) - Euro zone finance ministers are reviewing the size of the private sector's involvement in a second international bailout package for Greece, a move that could undermine the aid programme and hasten the threat of a Greek default.
Ministers also agreed after a meeting in Luxembourg that Greece could wait until mid-November until it receives the next installment from its existing emergency aid programme, piling more pressure on Athens to tackle its debt problems.
Jean-Claude Juncker, the chairman of the Eurogroup ministers, said they were reassessing the extent of the private sector's role in the planned second package for Greece, a centrepiece of the deal struck on July 21 to rescue Athens.
Under that deal, private creditors agreed to take a 21 percent write-down on their holdings of Greek debt via a plan to lighten the debt burden. Now that Greece's economic growth and deficit situation has worsened, that deal needs to be reviewed.
"As far as the PSI (private sector involvement) is concerned, we have to take into account the fact that we have experienced changes since the decisions we took on the July 21, so we are considering technical revisions, so yes," Juncker told reporters, although he would not elaborate.
Juncker also said the European Central Bank was not the main avenue being explored to increase the firepower of the European Financial Stability Facility, an acknowledgement that is likely to undermine confidence that the bailout fund can be sufficiently scaled up to calm febrile financial markets.
Despite more than six hours of talks, the meeting produced few concrete steps and is likely to provoke more uncertainty among investors, with expectations rising that Greece will end up having to default on its 357 billion euros of debts.
The only immediately positive development was that a months-long dispute over Finnish demands for collateral for new loan guarantees for Greece was resolved.
The next finance ministers' meeting on Oct 13, when they were expected to sign off on the next, 8 billion euro payment to Greece, has been cancelled, and EU and IMF inspectors will have several weeks in which to report back on Athens' budget cuts.
"Greece told us that the funds will have to be made available during the second week of November," Belgian Finance Minister Didier Reynders told reporters after the meeting, establishing a new, later deadline for the aid to be paid.
"We reviewed the Greek plan and we will now wait for the final report from the troika since we have time to decide."
Greece's admission on Sunday that it will miss its deficit target this year despite ever deeper cost-cutting measures provoked a sharp sell-off in stock markets and has raised new doubts over the second, 109 billion euro bailout.
European bank shares suffered the heaviest falls on fears that private sector bondholders may be forced to absorb bigger losses than agreed in a July rescue plan for Greece, which was based on more optimistic growth forecasts.
The worst performing bank was Franco-Belgian group Dexia , whose shares fell 10 percent on concerns over its heavy Greek exposure and after Moody's said liquidity problems could lead to a downgrade of its credit rating.
Greece's draft budget sent to parliament on Monday showed this year's deficit would be 8.5 percent of gross domestic product, well above the 7.6 percent agreed in Greece's EU/IMF bailout programme, the benchmark for future EU aid.
Finance Minister Evangelos Venizelos said the 2012 fiscal targets would be met in absolute terms and Greece would have a primary surplus before debt service for the first time in many years. That may be enough to convince the troika that the next, 8 billion euro tranche of aid to Athens can be paid.
However, next year's deficit is projected to be 6.8 percent of GDP, rather than the 6.5 percent EU/IMF goal, because the economy is set to shrink by a further 2.5 percent after a record 5.5 percent contraction in 2011.
A deeper-than-forecast recession means public debt will be equivalent to 161.8 percent of GDP this year, rising to 172.7 percent next year, by far the highest ratio in Europe.
The likelihood that Greece's funding needs next year will be greater than forecast when a second 109 billion euro rescue package was agreed in principle in July reopened a fraught battle over who should pay -- taxpayers or financiers.
Deutsche Bank (DBKGn.DE) chairman Josef Ackermann, head of the International Institute of Finance (IIF), which negotiated a "voluntary" bond-swap by investors as part of the bailout plan, warned at the weekend against changing the terms now.
"If we reopen the voluntary accord of July 21, we will not only lose precious time but quite possibly also private investor support," Ackermann told the Sunday edition of Greek newspaper Kathimerini.
"The impact of such a move will be incalculable. This is why I am warning in the most forceful way against any material revision," he said.
Private bondholders agreed to a 21 percent write-down on their Greek debt holdings but EU and German officials have suggested the "haircut" may have to be increased -- possibly to as much as 40 or 50 percent -- in light of a new funding shortfall and changed market conditions.
"Ultimately, Greece would need to see its debt written down by more and with that you need probably some kind of shoring up of the banking sector," said Alec Letchfield, chief investment officer at HSBC Asset Management.
Political resistance to pouring more public money into euro zone bailouts is growing across northern Europe.
"Greece is bankrupt," said Michael Fuchs, a deputy parliamentary floor leader in German Chancellor Angela Merkel's Christian Democrats, reflecting a growing mood in Berlin.
"Probably there is no other way for us other than to accept at least a 50 percent forgiveness of its debts," Fuchs told the Rheinische Post newspaper.
Uncertainty over the extent of damage to the already fragile European banking sector from a possible Greek default has been driving investors to take refuge in safer assets.
Yields on Spanish and Italian government bonds rose and the cost of insuring their debt against default spiked on the news from Greece, while money poured into safe-haven German Bunds. The euro fell to an eight-month low in Asia.
"The markets continue to conclude that a default for Greece is an inevitability and a question of when rather than if," said Nick Stamenkovic, strategist at RIA Capital Markets.
In Luxembourg, euro zone ministers discussed ways to leverage their EFSF bailout fund, but will not reach a conclusion on Monday, officials said. They also discussed how to maintain pressure on Greece to implement agreed structural reforms and privatisations to try to get its economy growing again -- one factor which might help it.
Economic and Monetary Affairs Commissioner Olli Rehn said Europe faced a triple challenge of "stalling growth, stressed sovereigns and still vulnerable banks".
Ministers would review options to enhance the financial firepower of the rescue fund, some of which involved leveraging with money from the European Central Bank, he said.
The debt and GDP projections illustrate how Greece has fallen into a vicious spiral of recession, falling revenues, soaring unemployment and declining consumer purchasing power.
Officials expect the next aid tranche