Three days after announcing that he and his government would quit, Czech Prime Minister Bohuslav Sobotka changed tack on Friday, saying he would instead seek the removal of his finance minister and political rival, Andrej Babis.

The latest twist in Czech politics comes amid a growing fight over Babis, a billionaire politician who faces questions over past business dealings but is also the most popular party leader before a parliamentary election in October.

Sobotka has been in office since 2014, with his leftist CSSD sharing power in a coalition government, which includes Babis' ANO.

Sobotka's backtracking came after President Milos Zeman, an ally of Babis, made it clear that he would treat the resignation as the prime minister's own - not the departure of the entire cabinet.

Accusing the president of making a "joke" of the Constitution, Sobotka told reporters: "In such a situation my resignation does not make any sense. The finance minister, burdened by extensive scandals, would remain in the government."

He added: "I will soon ask the president of the republic to recall the finance minister."

The president's spokesman, Jiri Ovcacek, tweeted: "A desperate prime minister is trying to pull the entire country into mud."

Political crisis

Babis, who is the Czech Republic's second richest citizen and worth $3.4bn according to Forbes, has denied Sobotka's allegations of tax fraud and refused to step down.

He heads the centrist ANO, which is tipped to win the October 20-21 vote.

READ MORE: Sobotka - Czech cabinet 'to quit' amid Andrej Babis row

Sobotka said he would formally send a request Friday to the president to fire Babis. The Constitution says the president dismisses ministers at the request of the prime minister, giving the head of state narrow room to manoeuvre.

The president's office said that Zeman will not act in haste, and will wait for the prime minister's move and act "responsibly".

Babis has called Sobotka's manoeuvring "ridiculous", telling the Reuters news agency that the prime minister's proposal to dismiss him violated the coalition agreement.

While a number of lawyers said the Constitution implied the prime minister's resignation means the fall of the entire cabinet, some experts have said it also allowed the interpretation that such a resignation, without a cabinet vote, might mean only the departure of the prime minister.

Prague-based political analyst Tomas Lebeda told the AFP news agency that Sobotka had become the victim of his own "ill-conceived decision", calling his move to quit a "huge error" just months before a general election.

"Instead of putting pressure on the president and the finance minister, the prime minister put himself under pressure," Lebeda said, adding that it was "extremely difficult to make any predictions."

The leaders of the three-party coalition are scheduled to meet next week over the crisis.