Talks between governments and private creditors about voluntary participation in a second bailout package for Greece will begin across the euro zone on Wednesday, a source in the German government said.

All relevant banks and insurers in Germany which could contribute to a private sector solution would take part in the talks, the source told Reuters.

The (German) finance ministry has invited banks and insurers for talks on a working group level in Frankfurt, the source said, adding the same would begin elsewhere in the euro zone.

Euro zone governments are discussing a second bailout package for Greece that would run from 2011 to 2014 and could amount to 120 billion euros, including up to 30 billion euros in private sector contributions on the basis of the so-called Vienna Initiative.

Chancellor Angela Merkel has taken criticism in the German press for softening her position during a meeting with French President Nicolas Sarkozy on Friday.

She agreed there that any private sector participation should be purely voluntary and address concerns of the European Central Bank.

In exchange for their support, German lenders have now demanded additional incentives in the form of state guarantees.

Banks in Germany have quantified their exposure at between 10-20 billion euros while insurers estimate their holdings are substantially less than 6 billion euros, or 0.5 percent of the 1.2 trillion euros in insurers' invested assets.

(Reporting by Gernot Heller, writing by Christiaan Hetzner and Eva Kuehnen; Editing by Noah Barkin and Louise Heavens)