The Czech Republic’s minority government has resigned, plunging the country into deeper political turmoil, as its recently installed prime minister, Andrej Babiš, fights allegations that he abused an EU subsidy programme a decade ago.

Wednesday’s resignation – a month after Babiš’ appointment – came a day after the government resoundingly lost a vote of confidence it had to win to stay in office.

It will continue as a caretaker administration while the Czech president, Miloš Zeman, decides what to do.

Zeman – a populist who has earned notoriety for xenophobic statements – had pledged to reappoint Babiš, a close ally, in the event of Tuesday’s confidence vote defeat, which had been widely anticipated.

But that promise may become meaningless because Zeman himself is now in political jeopardy after a worse than expected result in last weekend’s presidential election left him facing a nail-biting run-off against liberal opponent Jiří Drahoš next week.

Drahoš, 68, a former head of the Czech academy of sciences, has said he would not accept Babiš as prime minister because of charges filed against him by Czech police that one of his companies fraudulently obtained €2m (£1.75m) in European Union funds.

Babiš, 63, a billionaire tycoon who is the Czech Republic’s second-richest man, faces yet another potential setback when MPs vote on whether to remove his parliamentary immunity, which protects him from prosecution.

That possibility increased when a parliamentary committee voted on Tuesday in favour of stripping him of immunity before a vote in the full parliament, which will probably take place this week.

Babiš’s problems have compounded since last week’s leaked publication of a scathing 50-page report from the EU’s anti-fraud unit, Olaf, which alleged that multiple European and Czech laws were breached to win a small business grant for a countryside hotel and conference centre, known as Stork’s Nest, owned by his Agrofert conglomerate.

In a defiant press conference on Tuesday, the Slovak-born Babiš belittled the Olaf report and dismissed the charges as a fabrication by a “mafia” that he said had been robbing the Czech Republic.

“If I was not in politics, you would never hear about Stork Nest,” he said. “Of course, we will let parliament [strip us] of immunity. We live in a country where investigative institutions are independent.”

The most immediate threat to his political future may come from Drahoš, who finished second in a nine-man field in the first round of the presidential race with 26.6% of the vote, against 38.6% for Zeman. With the other defeated candidates now endorsing him and pledging their campaign resources, Drahoš is favourite to win the run-off on 26 and 27 January.

Drahoš has called having a prime minister who is facing charges “unacceptable” and said Babiš’s Action of Dissatisfied Citizens (ANO) party should not be given a second chance to form a government.

“If the ANO government does not win a vote of confidence at the first go, a member of another party should be invited to form a government,” he said.

Babiš’s predicament is a far cry from the strong position he appeared to hold after ANO – which campaigned against corruption and on opposition to the EU’s migrant relocation programme and adopting the euro – won nearly 30% of the vote to become the largest party in October’s parliamentary election. But other parties have refused to join a coalition because of the criminal allegations against Babiš, meaning that with just 78 out of 200 seats in parliament, it is unable to form a majority.

