Babis submitted the resignation to President Milos Zeman today.
Zeman, Babi's ally, accepted it and immediately asked Babis to try to form a new government again. He said he will swear him in as prime minister as soon as in February if he fails to get re-elected as president.
Any new government has to win a parliamentary confidence vote to rule.
Babis' centrist ANO (YES) movement won October's parliamentary election with 78 seats in the 200-seat lower house. But no other parliamentary party agreed to create a majority coalition government with ANO because they consider Babis unsuitable due to fraud charges linked to EU subsidies he faces.
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So far, the Communist Party has suggested it might be willing to tolerate a new ANO government. If that happens, it would be the first time that the Communists would get back to power at least indirectly since the 1989 anti-Communist Velvet Revolution.
But Babis would need more partners to secure a parliamentary majority.
"We will negotiate intensively and hopefully they will take us seriously," Babis said.
Zeman faces scientist Jiri Drahos in a presidential runoff vote over the weekend. Drahos said he would have a problem appointing as prime minister facing fraud charges. Zeman's term in office expires on March 8.