Slovak Interior Minister Robert Kalinak resigned on Monday, bowing to demands of a junior coalition partner which had sought the removal of Prime Minister Robert Fico's close ally amid a political crisis.
The death of Mr Kuciak, who probed fraud cases involving politically-connected businessmen, has stoked public anger over persistent corruption allegations and pushed Mr Fico's government towards collapse.
Should Most-Hid, a centrist group that represents the ethnic Hungarian minority in Slovakia, pull out of the ruling coalition, Fico will be forced to rule as part of a minority government that would need to rely on the backing of far-right lawmakers - something Fico's Smer party opposes.
Critics say Kalinak, who oversees the police as interior minister, can not guarantee an independent investigation into the killing of Kuciak and his fiancee in late February.
An estimated 50,000 people rallied in Bratislava on March 10 and thousands more in other cities to demand the resignation of Fico's cabinet and a full investigation of Kuciak and his fiance's deaths.
"My decision to resign is tied to our efforts to stabilize the situation", Kalinak said. It's not yet clear, however, if the move will be enough for the party, known as Most-Hid. That party's leadership will meet on Monday to decide whether it will remain in the coalition.