Kuciak was said to be preparing a report on suspected collusion between the Slovak government and Italian mafia. Mr Fico is the latest Slovak politician to resign as the fallout from the murder of a young journalist Jan Kuciak, continues to spread.
Robert Fico's resignation as prime minister has failed to appease a public outraged over the murder of 27-year-old investigative journalist Jan Kuciak, who reported on fraud allegations against businessmen with political ties.
On Thursday the long-serving Fico stepped aside, handing the government reins to a deputy after his leftist Smer party and its coalition partners agreed to a change of prime minister to keep the government going.
On Friday, protesters chanted "Early elections!".
"I can assure you that it will be a government that maintains its clear pro-European orientation", Pellegrini said in a statement.
The protests are the biggest in Slovakia since 1989, when the "Velvet Revolution" toppled the communist regime and resulted in secession and independence from the federation of Czechoslovakia. Third, a new head of the government must be chosen from members of the Fico-led Direction - Social Democracy party. More demonstrations are scheduled for Friday despite's Fico's move, said organizers who want to see a new election. Second, the coalition agreement between parties representing a majority in the parliament must be observed.
Protesters held banners calling for early elections and waved signs reading "Government Doesn't Work" and "Enough of Fico", according to Reuters.
More than 23,000 people said on Facebook they would still attend the rally in capital Bratislava, while thousands were expected to march in other towns.
Slovakia's next regular general election is due in 2020.