The prime minister, in power 10 of the past 12 years, has fought to keep his three-party government intact.

Earlier on Monday, Fico's protege and closest ally in his Smer party, Interior Minister Robert Kalinak, said he would resign - which Most-Hid had demanded since last week.

However, with street protests growing, Most-Hid raised its demands on Monday.

Fico's coalition holds a narrow majority of 78 seats in the 150-member parliament. Fico could still seek to rule in a minority without Most-Hid but faces limited options for support.

The leader of the third coalition member, the Slovak National Party (SNS), said earlier his party would want an early election if the coalition loses its majority.

SNS and Smer are expected to react to Most-Hid's decision on Tuesday, Slovak news websites reported.

Opposition parties, also wanting early elections, have sought a no-confidence motion against Fico's government and need 76 votes to topple it. Bugar said it was too early to say how his party would vote on such a motion.

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He said he would seek a deal for the coalition to call an early election on its own terms.

For an early election, 90 votes in parliament are needed.

The killing of reporter Jan Kuciak, shot dead at home with his fiancee, and his reporting have swelled public anger over corruption in the European Union member country.

Slovakia has prospered in the past decade, joining the euro zone and growing at one of the fastest rates in Europe, but many see Fico as having failed to fight graft and cronyism.

Many of Most-Hid's lawmakers were also angered last week when Fico began referring to what the party called "conspiracy theories".

Echoing Hungarian Prime Minister Viktor Orban, Fico has accused foreign forces of trying to destabilise Slovakia and has questioned the president's meetings with financier George Soros in New York last year.

After an estimated 50,000 people rallied in the capital Bratislava last Friday, and thousands more in other cities, another protest is planned for Friday.

Kuciak focused on tax fraud involving politically connected businessmen. Before he was killed, he had been investigating Italian businessmen in Slovakia with suspected mafia links. One of the Italians Kuciak wrote about had co-owned firms with two Slovaks who went on to work in Fico's office.

Both have resigned but deny links to the murder. Their Italian former business partner denies connections to the mafia. No one has been charged in the killings.

In seeking the interior minister's resignation, critics had said Kalinak, who oversaw the police, could not guarantee an independent investigation into Kuciak's death.