Greece is nearing an agreement with private-sector bond holders on a debt swap crucial to a second bailout package for Athens, the European Union's top economic official said on Tuesday.

EU Economic and Monetary Affairs Commissioner Olli Rehn also warned that the euro zone's financial crisis was not over, and urged financial markets to be patient for the fruits of reforms to avoid pushing the bloc into a liquidity crisis.

Some bankers have sounded sceptical over the private-sector participation for Greece, which the leaders of France and Germany on Monday reiterated was essential, and Rehn was cautious.

We are about to finalise shortly negotiations on private-sector involvement, which is a necessary condition for the second programme, Rehn told the European Parliament. It is not going to be easy but I am reasonably confident we will achieve this aim.

Greek Deputy Finance Minister Filippos Sachinidis said on Tuesday there was progress but no deal yet in the bond swap talks with creditor banks and reaffirmed Athens' aim for a voluntary accord that made the country's debt sustainable.

r Under a so-called private sector involvement (PSI), a key part of a second 130 billion euro Greek bailout deal, investors would voluntarily accept a nominal 50 percent discount on Greek bond holdings in return for a mix of cash and new bonds.

Saddled with some huge debts and split by political differences, euro zone nations have seen the debt crisis push the regional economy towards recession.

Rehn, one of the EU's most powerful commissioners, is charged with policing the 27-nation bloc's national budgets, and is insisting on fiscal rigour -- which some economists say is strangling economic growth and putting Europeans out of work.

Rehn acknowledged the difficulties and asked for patience waiting for results of his tough medicine for debt reduction.

The crisis has damaged the European economy and affected the jobs and the welfare of Europeans, and this crisis is by no means behind us, Rehn said. It will take time, structural reforms often take a long time... Markets, however, tend to be impatient and this impatience can push sovereigns or banking institutions into a liquidity crisis.

The euro zone, which accounts for about 16 percent of world output, is forecast to struggle to grow in 2012 and could contract by as much as 1 percent, with its impact reverberating to the United States and Asia.

The sine qua non necessary to return to the path of economic growth is that we will be able to resolve the sovereign crisis and the banking sector problems, Rehn said.

(Reporting By Robin Emmott and Jan Strupczewski; editing by Sebastian Moffett and Stephen Nisbet)