Slovak President Andrej Kiska said he would seek talks with political parties and a new government or early elections could be options to renew public trust following the case of a murdered investigative journalist that has shaken the nation.

The president, who does not have formal powers to dissolve the government, accused senior officials of an "arrogance of power", and bemoaned a lack of action on the part of the government to restore public trust and defuse tensions after the killings last weekend.

He said he would meet political parties to find a way out.

But Prime Minister Robert Fico disagreed, accusing the president of "dancing on the graves" of the victims.

Thousands of people marched in Bratislava and other Slovak cities on Friday for journalist Jan Kuciak, who had been looking into suspected mafia links among Italian businessmen in eastern Slovakia before he was found shot dead last weekend.

The murder of Kuciak, whose reporting focused primarily on links between businessmen and Slovak politicians, was the first of a journalist in the country.

Thousands marched in Bratislava and other Slovak cities on Friday, demanding swift action in response to a killing that has shocked the country and shaken its government.

His last, unfinished article was published posthumously by Slovak and international media. One of the men named in Kuciak's report, which probed potential abuse of European Union subsidies and other fraud, had past links to people who subsequently worked for Prime Minister Robert Fico's office.

The murder prompted demands from Fico's coalition partners for the resignation of senior officials.