"Following the second round of local elections (on June 2), I will ask the president to immediately call national elections," Tsipras said in a televised address.
A likely date for the ballot is June 30, news reports said.
With about a third of polling stations accounted for, Tsipras' leftist Syriza party scored less than 24 percent in the European ballot compared to more than 33 per cent for the main opposition conservative party New Democracy.
And in local elections, early results showed New Democracy in control, or securing outright, the bulk of Greece's 13 regions.
"The electoral result... is not worthy of our expectations," he said.
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