* Murder of investigative journalist shakes nation
* Journalist Kuciak specialised in exposing corruption
* New street protests set for Friday
* Junior coalition party calls for early election (Updates with status of talks)
By Tatiana Jancarikova
BRATISLAVA, March 13 (Reuters) - Slovak Prime Minister Robert Fico faced pressure on Tuesday to agree to an early election with his coalition crumbling in the face of mass protests prompted by the murder of a young journalist who specialised in exposing corruption.
The central European nation stumbled into crisis late last month with the killing of Jan Kuciak, who focused on tax fraud involving politically-connected businessmen, and Slovakia's interior minister resigned on Monday.
Last week saw the largest street protests in Slovakia since the end of communist rule nearly 30 years ago, and organisers promised new demonstrations for Friday.
The centrist Most-Hid (Bridge), a party representing the ethnic Hungarian minority, said on Monday it wanted a deal on a snap election or it would quit the three-party coalition of Prime Minister Robert Fico.
The parties held talks on Tuesday but without result.
Midway through a third term, Fico now faces calls to quit, a blow to the long-time prime minister who has sought to stand out from largely eurosceptic leaders in central Europe by pushing the country of 5.4 million closer to the European Union's core.
His Smer party, winner of the past four elections, has long held a big lead in opinion polls thanks to a mix of keeping deficits in check while giving handouts to voters such as free train tickets for students and pensioners.
But the journalist's murder has focused popular anger on Fico over his perceived failure to corruption and cronyism.
His other coalition partner, the Slovak National Party (SNS), which has moved from the far right towards the centre in recent years, said on Tuesday it would only discuss an early election if the government fell apart.
Fico's coalition holds 78 seats in the 150-member parliament. It will face a no-confidence vote, filed by the opposition, next Monday and 76 votes would topple it.
For an early election, 90 votes in parliament are needed.
The political fallout from Kuciak's killing has badly tarnished Fico, in power for much of the past 12 years during which Slovakia's economy has grown rapidly as international carmakers have set up factories there.
It is the only formerly communist central or eastern European state in the euro zone, entering in 2009.
Just before he was found shot dead along with his fiancee at his house outside of Bratislava, Kuciak had been looking into suspected mafia links of Italians with businesses in Slovakia.
One of the Italians had past business links with two Slovaks, including a former model, who later worked in Fico's office. Both have resigned but deny connections to the murder.
Their Italian former business partner has denied having connections with the mafia. No one has been charged over the killing of Kuciak and his fiancee.
Interior Minister Robert Kalinak, a Fico protege, resigned on Monday - a step Most-Hid had demanded to calm the situation.
Despite this, two sources in Most-Hid said growing protests along with Fico's combative rhetoric following the murder had driven the party to Monday's decision.
Echoing Hungarian Prime Minister Viktor Orban, Fico has accused foreign forces of trying to destabilise Slovakia and has questioned the Slovak president's meetings with financier George Soros last year.
Analysts see increasing chances of an early election that Smer could again win, though a minority government of Smer and SNS was just as possible, with the support of independent lawmakers or the far right People's Party-Our Slovakia.
"Smer may still win the early election despite the loss of some voters. But Fico's aggressive communication weakens its coalition potential," political analyst Aneta Vilagi said. (Reporting by Tatiana Jancarikova Writing by Robert Muller and Jason Hovet Editing by Mark Heinrich)
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