Robert Fico's surprise move was meant to keep the current three-party coalition in power and prevent possible early elections.
Slovak Prime Minister Robert Fico offered to resign as early as Thursday if the country's president allows his party to remain in charge of the government and continue its term.
The country's president, Andrej Kiska, had pushed for an election to solve the country's worst crisis since its split from the Czech Republic in 1993.More news: Annual Wichita Falls Egg Hunt Saturday
Police said Kuciak's death was "most likely" related to his investigation on ties between Slovakia's top politicians and Italy's 'Ndrangheta mafia.
Slovakia has witnessed its largest protest since anti-communism rallies in 1989, with an estimated 50,000 gathering in the capital, Bratislava.
Jan Kuciak, 27, was investigating government corruption when he was killed.
The murder and Kuciak's article, published after his death, sparked a wave of anti-government sentiment in Slovakia, an European Union and North Atlantic Treaty Organisation member of 5.4 million people. According to Kuciak's last unfinished story, one of the businessmen had worked with two people who worked in Fico's office.More news: Big Bang's Seungri reveals enlistment plan
"The top priority for all of us must be to carry out an independent and thorough investigation of the facts and bring those responsible to justice", the EU's security commissioner Julian King told MEPs in Strasbourg today. "They have failed to investigate all previous scandals".
The prime minister urged Kiska to "respect" the cabinet as a first condition for his resignation.
But a minor member of Slovakia's three-way governing coalition, the Most-Hid party, raised the pressure further, calling for early elections. Instead, demonstrators have called for a "new trustworthy government". But that's not what protesters have demanded.
Analysts believe Fico is unlikely to make out of the ensuing political crisis.More news: 'The Cher Show' sews up costume designer Bob Mackie