Former energy minister Panagiotis Lafazanis, who heads the newly formed Popular Unity, received the maximum three-day mandate from the country's president after the head of the main opposition conservative New Democracy failed to form a government.
Greek banking stocks were the worst hit with Alpha Bank, Attica Bank and Eurobank Ergasius, Bank of Piraeus and the National Bank of Greece were all trading around 30 percent lower - the daily volatility limit.
Greece is preparing to reopen its stock exchange and allow international investors to take their money out of the country's listed companies after a one-month shutdown.
The impasse forced eurozone finance ministers to cut short a meeting yesterday which they plan to resume today. Concern over the lack of progress weighed on financial markets, with stock indexes falling in the US, where trading was still open.
Sarah Hewin of Standard Chartered says the dire risks that the market was concerned about this time last year have receded for the moment.
Greece's prime minister failed to convince opposition leaders on Friday to support tougher austerity measures to free up EU/IMF aid needed to avert a debt default.