Greece's prime minister offered to quit and make way for a national unity government after mass protests against a new austerity plan turned violent on Wednesday, with the country teetering on the brink of default.

Senior government sources said Socialist Prime Minister George Papandreou told the leader of the conservative opposition he would be willing to step aside if a unity cabinet agreed on a clear plan to meet the terms of an IMF/EU bailout.

Prime Minister Papandreou talked with Mr (Antonis) Samaras today and proposed that if the two agreed on a framework of specific commitments for change in the country and the political system and specific targets, he would be willing to stand down from his office, one government source said.

The dramatic move came after euro zone finance ministers failed to agree on how to involve private investors in a second financial rescue for highly-indebted Greece, and senior EU officials said a deal was now unlikely to be reached at a summit next week and was likely to be delayed until mid-July.

Tens of thousands of angry Greeks massed outside parliament to demonstrate rising hostility against draconian spending cuts required to win a second bailout.

Rioters hurled petrol bombs at the finance ministry and police fired volleys of tear gas in clashes in the main Syntagma Square as protesters tried to stop lawmakers adopting new tax rises, spending cuts and sell-offs of state assets.

Growing risks to the Greek budget plans and signs of deep divisions over the role private creditors should play in a new aid package pushed the euro to a two-week low against the dollar and sent bond yields of peripheral euro states rocketing.

Doubts about the bloc's ability to solve its debt woes also hit European banking stocks.

NO POSITION TO RENEGOTIATE

Greek banks fell by as much as 7 percent on growing political uncertainty and shares in top French banks tumbled after credit ratings agency Moody's said it might downgrade them because of their exposure to Greece's debt-stricken economy.

Papandreou's PASOK party still has an absolute majority in parliament but public support is dwindling, backbench lawmakers are starting to defect and several ministers are unhappy about privatizations imposed by international lenders.

An official of the opposition New Democracy party said a unity government was only possible if Papandreou resigned and the EU/IMF bailout were renegotiated. [ID:nATH006160]

However, Greece is in an extremely weak position to renegotiate anything since it faces default in July unless it receives the next tranche of emergency loans.

That is on hold until Athens adopts the tougher austerity package demanded after it fell behind on its first 110 billion euros ($158.1 billion) rescue plan.

Even if you look at the best case scenario, where we get parliamentary approval in Greece and the EU agrees a new aid package, you still have big medium-term issues, said Jacques Cailloux, an economist at RBS in London.

The political uncertainty is not going to go away, there are implementation risks, privatization risks, you name it.

The new package includes tax hikes and spending cuts totaling 28 billion euros through 2015. It also aims to raise 50 billion euros through privatizations.

The European Commission said it still expected Greece to receive the 12 billion euro aid tranche it needs next month to pay maturing debt.

DELAY TO JULY

In Brussels, finance ministers of the 17-nation single currency area argued late into Tuesday night over how to make private bondholders share the cost of the second rescue in two years without triggering even worse financial turmoil.

They had been aiming for a deal at a European Union summit on June 23-24, but Slovak Finance Minister Ivan Miklos said on Wednesday that agreement could be delayed until July 11.

A spokesman for German Finance Minister Wolfgang Schaeuble insisted an agreement was still expected next Monday, but senior EU officials and diplomats in Brussels said that barring a last-minute Franco-German breakthrough there was not enough time to resolve the complex issue on private sector involvement.

The impasse weighed heavily on markets, pushing the cost of insuring Greek debt against default to an all-time high and the euro below $1.43 for the first time since late May.

European paymaster Germany is insisting the banks, pension funds and insurance firms that hold Greek debt swap their bonds for new ones with maturities that are seven years longer.

Fearful that this solution would prompt rating agencies to label Greece in default, the European Central Bank, European Commission and France all favor a softer option in which holders of Greek bonds would be asked to buy new Greek debt as their holdings mature.

But ratings agency Fitch said on Wednesday it would view even a voluntary rollover of this sort as a distressed debt exchange and be forced to lower Greece's rating to restricted default once such a transaction was completed.

The other major ratings agencies have taken a similar line.

This could mean European governments will need to provide more of the estimated 120 billion euros in funding they are aiming to secure for Greece, including privatization revenues.

That could be unacceptable to northern euro zone creditor states like Germany, the Netherlands and Finland, which are all demanding private sector burden-sharing in response to strong public opposition to further taxpayer-funded bailouts.

German Chancellor Angela Merkel will meet Mario Draghi, the anointed successor to Jean-Claude Trichet as president of the ECB, on Thursday in Berlin to try to resolve the impasse.

A meeting between Merkel and French President Nicolas Sarkozy is planned for Friday.

Markets are overwhelmingly skeptical that Greece can ever repay its debt mountain, which has reached 340 billion euros or 150 percent of the country's annual economic output. Many expect a painful debt restructuring in the years ahead, regardless of what governments agree over the coming weeks.

(Additional reporting by George Georgiopoulos, Harry Papachristou and Ingrid Melander in Athens, Ana Nicolaci da Costa in London and Lionel Laurent in Paris; writing by Paul Taylor and Noah Barkin, editing by Mike Peacock)