In 2011, Mr. Babis founded his own political party, ANO (the name means “Yes” in Czech), and in the 2013 parliamentary elections, the party placed second, behind Mr. Sobotka’s Social Democratic Party. The parties formed an uneasy coalition, and Mr. Babis was named finance minister.
In January, the Czech establishment teamed up against Mr. Babis, enacting a law that would bar cabinet ministers from owning media firms or more than one-quarter of any company seeking government contracts or European Union subsidies. Mr. Babis responded by declaring that he would place his business holdings in a trust.
The controversy involves corporate bonds that Agrofert issued in 2012 under a program that allowed buyers of the bonds to enjoy a tax exemption on the interest. Mr. Babis bought some of the bonds himself. The authorities are looking into how he obtained the money to buy the bonds, and whether he benefited improperly from the transaction.
Mr. Sobotka said that Mr. Babis had set a bad example.
“It is unacceptable for the finance minister not to be able to prove the origins of his property, especially since he is a member of a government that has built its program on a fight against tax evasion,” Mr. Sobotka said at the news conference. “It is impossible for the government to chase small entrepreneurs when a billionaire is evading taxes.”
Mr. Sobotka said it was a difficult decision. “If I ask the finance minister to resign, I might turn him into a martyr in the upcoming months,” the prime minister said. “He has been preparing for that role for the past few days already. I chose the only possible decision.”
Petr Fiala, the head of the center-right opposition Civic Democratic Party, ridiculed Mr. Sobotka’s logic, calling it an example of “cluelessness.” He predicted that Mr. Sobotka would not be able to form a governing coalition without Mr. Babis’s support.
“The prime minister’s decision is a continuation of an absurd political theater that we have been witnessing for a few months now,” Mr. Fiala said in an interview. “One has to wonder how the prime minister plans to negotiate with the current coalition parties — that is with Andrej Babis, as well — about a new government without Andrej Babis.”
Mr. Babis, for his part, said he was stunned by the decision.
“The prime minister just destroyed one of the most successful governments since the Velvet Revolution,” he said in a statement, referring to the nonviolent demonstrations in 1989 that eventually toppled one-party Communist rule in what was then Czechoslovakia.
Mr. Babis said he had sent a letter to Mr. Sobotka explaining that he had complied with all tax laws.
“Mr. Sobotka has never run any business of his own, so I understand it is difficult for him to comprehend the letter I sent,” Mr. Babis said.
The Czech Republic joined the European Union in 2004, and it has experienced rapid economic growth, It also has one of the lowest unemployment rates — 3.2 percent in March — of the 28 nations in the bloc. The Czech currency, the koruna, dipped slightly on Tuesday against the euro after news of the resignations, but it quickly recovered.
Analysts said that Mr. Sobotka might have made a shrewd decision by distancing himself from Mr. Babis.
“It was a very good move of Sobotka that will free his hands for the election campaign, allow him to stand up against Babis and allow him to claim that he is not clinging to power,” said Stanislav Balik, the head of the political science department at Masaryk University in Brno, the second-largest Czech city, after Prague. “The big unknown now is the president. Who will he give power to?”
Mr. Zeman, who said through a spokesman that he had no immediate comment, could reject the resignations and insist that the current cabinet stay on until the elections. Or he could ask someone other than Mr. Sobotka to try to form a caretaker government. (Mr. Babis said on Tuesday that he had no interest in doing so.)
“We might have a new government next week, or we might have to wait for five more months,” Mr. Balik said, referring to the fall elections.