Tsipras announced his resignation on Thursday to pave the way for early elections he hopes will secure support for a third bailout deal with Greece’s creditors.
Tsipras and Syriza swept into power in January on a platform to abolish unpopular austerity measures that have only been strengthened in the recent deal.
Speaking to reporters over the weekend, Lafazanis ruled out cooperation with other parties over "unbridgeable" differences, effectively conceding that Popular Unity would fail to garner majority support to form a coalition.
The leader of Greece’s second-largest opposition party New Democracy, Evangelos Meimarakis, has failed to take advantage of the three-day mandate to form a 151-majority ruling coalition in the 300-member legislature over the weekend.
Following Tsipras’ resignation, Greece will hold early elections next month, reportedly as early as September 20.