Slovak President Andrej Kiska has accepted the resignation of Robert Fico from the prime minister's post in the wake of a public outcry resulting from the murder of investigative journalist Jan Kuciak last month.

Speaking at the presidential palace after a meeting with the president on Thursday, Fico announced that his deputy prime minister, Peter Pellegrini, has been put forward to take the reins and establish a new government.

"The nomination of Peter Pellegrini is the most natural thing," said Fico.

Fico said he was sure that forming a new government is the "right step, as early parliamentary elections would not have had any stability."

While Fico has resigned from the prime minister's post, he said he would remain with the party and still be very much present at political events.

On February 25, Jan Kuciak and his fiancee, Martina Kusnirova, both 27, were found shot dead at their home near Bratislava in what police described as "most likely" related to his investigative work.

At the time, he had been investigating an alleged connection between Italy's 'Ndrangheta crime syndicate and high-ranking officials in the Slovak government.

The story was published posthumously by Kuciak's news outlet, Aktuality.

The double-murder sparked a nationwide outcry, with tens of thousands of Slovaks calling for an end to corruption in some the country's biggest demonstrations since the fall of the Iron Curtain in 1989.

Police had initially questioned suspects over the killings, but no arrests have been made.

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With pressure mounting on Fico, both President Kiska and a minor member of the ruling coalition Most-Hid Party called for drastic reform or snap elections.

On Monday, Robert Kalinak resigned as interior minister in an effort to prevent the government from collapsing.

Kiska supported Fico's offer to resign on condition that his party be allowed to pick the next government leader in an attempt to preserve the three-party government, government officials said on Wednesday.

The condition has drawn sharp criticism from the opposition and political experts who claim Fico is attempting to retain his influence while also threatening Slovakia's democratic institutions.

"Civil society is not only asking for the resignation of Mr Fico himself, the demand here is for the change of politics of which Mr Fico is a symbol and the frontrunner, said Martin Poliacik, a member of parliament with the new Progressive Slovakia movement.

Viera Zuborova, executive director of the Bratislava Policy Institute, a Slovak think-tank, said the situation harkens back to the final days of the Soviet-aligned government's attempts to cling to power in 1989.

Fico's demands to the president and subsequent retention of power are "unique in modern Slovak history", she said, adding that installing Pellegrini without an election was not in the spirit of democracy.

Currently, regional elections are slated for November with MEP and presidential elections to take place in 2019.

Nationwide protests, meanwhile, are expected to continue tomorrow.