Prime Minister Andrej Babiš (ANO) and Social Democrat (ČSSD) chairman Jan Hamáček failed to find common ground at a meeting Monday over the appointment of a new Minister of Culture.
Hamáček said the Social Democrats, the junior coalition party, insist on their candidate, Michal Šmarda, and say President Miloš Zeman is violating the Constitution by failing to appoint him.
President Zeman said last week that Mr Šmarda was unqualified for the job, a view PM Babiš said on Friday that he shared.
Critics say the president is trying to exercise undue political power through his largely ceremonial position. He and Mr Babiš are due to meet to discuss the situation on Tuesday. The Social Democrats have threatened to quit the government if their candidate is not appointed.