One of Czech ruling coalition parties, the Social Democrats, threatened to quit in protest at President Milos Zeman's refusal to appoint a new culture minister from their ranks.
They have called on Babis to press the president to make the appointment. But Zeman has told he prefers the current minister.
Czech Prime Minister Andrej Babis said on June 30 there would be a snap election if his coalition partner quits, raising the prospect of more political turmoil after weeks of street protests against his rule.
"I believe the Social Democrats will not leave the government," Babis said, referring to his left-leaning junior coalition partner.