Slovakia has been thrown into crisis after the murder in late February of a journalist probing corruption, sparking the largest street protests since the end of communism almost three decades ago and pushing Fico's government to the brink.
Interior Minister Robert Kalinak told reporters on Monday he hopes his resignation, sought by the opposition and the junior coalition Most party, will help to stabilize the country's political situation.
Fico's Smer party has been ahead in opinion polls, with 25.5 percent support in Focus agency's January survey, nearly double the opposition SaS party in second place.
At the same time, it may provide a release valve on pressure against the premier, who's the latest eastern European Union leader to face public outcry. Fico has defied calls from demonstrators and President Andrej Kiska to give way to early elections in the euro-area country of 5.4 million.
"It's important for stability to be maintained, therefore I made a decision to resign the post of deputy prime minister and interior minister", Mr Kalinak said. Fico's coalition holds a narrow majority of 78 seats in the 150-member parliament. However, with street protests growing, Most-Hid raised its demands on Monday. The party welcomed Kalinak's resignation although its leader, Bela Bugar, declined to comment when asked whether it would be enough to remain in the coalition.
Police have said Kuciak's death was "most likely" related to his investigation resulting in an article on ties between Slovakia's top politicians and Italy's notorious 'Ndrangheta mafia, which his employer posthumously published.
Kuciak focussed on tax fraud involving politically-connected businessmen.
Fico's alleged link to the mafia was his close aide Maria Troskova, a former model and Miss Universe contestant who used to be close to businessman Antonino Vadala, one of the detained Italians. One of the Italians Kuciak wrote about had co-owned firms with two Slovaks who went on to work in Fico's office. Both have denied wrongdoing.
"If these negotiations with coalition partners are not successful, Most-Hid will leave the government coalition". Many of its lawmakers were angered last week when Fico began referring to what the party called "conspiracy theories".
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.