Bela Bugar, chairman of the Most-Hid party of mostly ethnic Hungarians, said that if its two governing partners don't agree to negotiate an early vote, his party is ready to leave the coalition. Its leadership is meeting later Monday.
Bugar's announcement means the government created after the 2016 general election could fall apart soon.
Slovak Deputy Prime Minister and Interior Minister Robert Kalinak resigned on Monday in wake of the mass demonstrations triggered by the killing of Ján Kuciak and his fiancee.
President Andrej Kiska also has proposed early elections or substantial changes in the government as a way out of the crisis.
On Friday, an estimated 50,000 people rallied in Bratislava and thousands more in other cities to call on Slovakia's Prime Minister, Robert Fico, to dismiss his closest ally, Robert Kalinak.
Fico's three-party coalition, which also includes the centrist Slovak National Party (SNS), has 78 of 150 seats in parliament. "For this reason I have made a decision to resign as deputy prime minister and interior minister". Kalinak's resignation was a key requirement of Most-Hid for it remaining in the coalition.
"The murders of journalist Jan Kuciak and his fiancee Martina Kusnirova were very hard for me to come to terms with", Kalinak said at a press conference. Kalinak's move to quit is one of Fico's biggest political sacrifices of his three terms in power as he is also losing the man who was best placed to replace him at the head of his Smer party.
Thousands already demanded Kalinak's resignation past year after he was linked to earlier corruption scandals.
The Central European nation has been swept by massive protests since the murder of journalist Ján Kuciak, who was behind a report unveiling links between Slovakian lawmakers and organized crime groups.
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