The crisis was prompted by the deaths of Jan Kuciak and his fiancee Martina Kusnirova.
Robert Fico said he would quit today but set out several conditions, including the right to nominate a successor from his party.
Mr Fico says he is ready to resign if the next prime minister is from his leftist Smer-Social Democracy party and presents his or her name on Thursday.
Robert Fico's surprise move was meant to keep the current three-party coalition in power and prevent possible early elections. Their murders sent shockwaves across the country and the EU.
AFP 2018 JOE KLAMARSlovak Interior Minister Steps Down After Journalist's Murder
The assassination provoked mass protests with an estimated 50,000 people rallying in Bratislava and thousands more in other cities demanding a thorough investigation into the journalist's murder and the resignation of the government.
Kuciak's murder has pushed growing frustration to a fever-pitch, with protesters saying the government can't be trusted to properly investigate the crime.
Slovak President Andrej Kiska, considered a political rival of the prime minister, said the country is facing a crisis of trust. Instead, demonstrators have called for a "new trustworthy government". Martin Slosiarik of the Focus polling agency told Reuters news agency.