The Social Democrats want the current culture minister to be dismissed but the president is refusing to approve the dismissal, creating a standoff that could topple the government.
The Czech government led by the populist ANO party on Thursday survived a vote of no confidence in parliament after massive protests against Prime Minister Andrej Babis.
The Million Moments for Democracy group is calling for Andrej Babis to quit over allegations that he fraudulently uses his power as Prime Minister to boost his own business interests.
Hundreds of thousands rallied in Prague on Sunday to demand the resignation of Czech Prime Minister Andrej Babis in the biggest public confrontation with the government since the 1989 Velvet Revolution.
Organisers say up to 120,000 people have protested in the Czech capital Prague calling for the resignation of Prime Minister Andrej Babis.
The government survived a vote of no-confidence over fraud allegations implicating the Prime Minister which he denies.
Billionaire Andrej Babiš has been appointed as Czech PM despite large protests about his former Communist links