Launched by Geneva trade union activist Paolo Gilardi, the petition claims Greek tax evasion amounts to €550 billion (666 billion francs, $710 billion) -- 2.5 times the crisis-hit country's GDP -- and "part of this money is sitting in Swiss banks."
In a call to the Federal Council, the petition notes that Switzerland recently sent thousands of names of United States citizens with Swiss UBS bank accounts to the Washington tax authorities as part of a US probe into tax dodging.
"Today, we ask you solemnly to do the same to help save the Greek people," the petition reads, adding that the money in Swiss banks was responsible for "making the Greek people even hungrier."
The development comes as negotiations continue between Switzerland and Greece for an agreement on the issue of tax evasion.
As part of the deal, Greek individuals with non-declared funds in Switzerland would maintain their anonymity, but their assets would be taxed by Bern, which in turn would transfer the revenues to Athens.
But Greece turned its back on the deal on October 1st after getting hold of a CD containing names of Greek nationals with undeclared Swiss bank accounts, according to a statement from the Greek Finance ministry.
Greece has not released any estimation of undeclared Greek funds placed in Switzerland, although Greek media estimates vary wildly, from €2 billion to €200 billion..
In 2011, the Swiss National Bank estimated that Greek nationals placed assets worth €3.5 million in Switzerland's banks, an increase of €1.2 billion from 2010, according to news agency ATS.
Ahead of the present initiative -- the first step towards it becoming law in Switzerland -- the Association of Swiss Bankers (ASB) rejected a call from Greece to release details of Swiss bank accounts held by Greek nationals.