* Euro zone officials agree new bailout in principle-source
* Private creditors may participate modestly in new scheme
* Leftists stage protest at Finance Ministry
* Papandreou to present mid-term budget plan to Juncker (Adds finance ministry, report on funding figures)
By Lefteris Papadimas and George Georgiopoulos
ATHENS, June 3 (Reuters) - Greece is set to impose a deeper bout of austerity on its struggling economy and promise to speed up a privatisation drive in return for a new international bailout to avoid a debt default.
Prime Minister George Papandreou on Friday will present his side of the deal, a medium-term budget plan, when he meets the chairman of euro zone finance ministers -- the people who must stump up much of the planned new funding along with the IMF.
In Athens leftists staged a protest at the finance ministry, hanging a huge banner across the building to denounce policies which they said would "turn workers into modern slaves".
Euro zone officials meeting in Vienna agreed in principle to a new three-year programme for Greece to run until mid-2014, a source close to the negotiations said late on Thursday.
This would effectively supersede a 110 billion euro rescue Greece agreed with the European Union and IMF a year ago.
But whereas taxpayers have so far borne the brunt of rescuing Greece and fellow euro zone members Ireland and Portugal, the new deal would involve some participation of private sector investors, the source told Reuters.
Some European politicians have argued that investors who bought Greek government bonds will have to share that burden, perhaps in the form of cutting the value of their debt.
The European Central Bank has fought such an idea, fearing this could provoke a crisis among European banks which hold large sums in Greek debt, and lead to a violent reaction on financial markets far beyond Greek borders.
However, participation of private sector investors in the new deal would be limited to avoid triggering a "credit event", the source said, without providing any figures.
One scenario, the Greek newspaper Kathimerini reported, is for the bailout to total 85 billion euros over three years up to 2014, with the EU and International Monetary Fund contributing more than 30-40 billion euros.
"The rest will come from the private sector and privatisation proceeds," Kathimerini said. The most likely option is that private creditors, mainly banks, will be called to swap their bonds with new ones maturing 10 to 15 years later.
"The aim is for the private sector's participation to be voluntary and in a form that will not be considered a default."
Athens, which is struggling to lower its budget deficit, let alone its 340 billion euro debt mountain, hasn't got a done deal yet. Anything agreed by the officials in Vienna must be approved by the euro zone finance ministers, some of whom represent electorates which are hostile to any more aid to Greece.
Papandreou starts the offensive to win political approval when he meets Eurogroup chairman Jean-Claude Juncker in Luxembourg.
"The prime minister will present the main points of the mid-term plan to Juncker, which include speedier privatisations and new measures to cut government spending and raise revenues," a senior Greek government official said.
Greeks are already suffering under waves of austerity imposed after Athens had to seek its first bailout from the European Union and IMF a year ago.
Activists from the Communist-affiliated PAME group got into the finance ministry, which stands on Syntagma Square where protesters gather nightly to demonstrate against corruption and economic mismanagement.
"Organise and fight for an overthrow -- General Strike", read a banner draped from the roof by PAME, which advocates non-violent protest. The Greek flag remained flying from the building but next to it, PAME banners had replaced the usual circle of yellow stars on a blue background of the EU.
"We have a sacred duty to our children and ourselves to cancel plans to turn workers into modern slaves," PAME said in a statement. "We must not allow our children to work for hunger wages. If we do not fight to overthrow these policies their working future will be hell."
Greece's main public sector union, ADEDY, will join private sector sister union GSEE in a nationwide strike on June 15.
The Greek government official said Athens had signed up to 6.4 billion euros ($9.23 billion) in new measures to cut its 2011 budget deficit and aimed to wrap up bailout talks with a team of international inspectors by Friday. (Additional reporting by Paul Taylor in Paris, Angeliki Koutantou and Ingrid Melander in Athens; Writing by David Stamp, editing by Patrick Graham)