"We think that only early elections would solve this situation", said Bela Bugar, chairman of Most-Hid on Monday evening after an eight-hour internal party discussion.
Kalinak's move comes after tens of thousands of protesters across Slovakia demanded the resignation of the government and a thorough investigation into the shooting deaths of Jan Kuciak and Martina Kusnirova.
President Andrej Kiska also has proposed early elections or substantial changes in the government as a way out of the crisis.
Slovakia's Interior Minister Robert Kalinak has resigned amid a political scandal caused by the murder of a journalist and his fiancée.More news: Keenum Preparing to Sign with Denver
The killings have gripped Slovakia, leading to calls for an investigation and to anti-government protests in Bratislava on Friday which were thought to be the largest in the country since the fall of Communism in 1989.
Mr Fico initially resisted attempts to remove Mr Kalinak but had suggested last week a willingness to compromise to keep Most-Hid's support. Fico is leader of the leftist Smer-Social Democracy party.
The coalition, which also includes the Slovak National Party, has a slim majority of 78 deputies in 150-seat parliament, including 14 lawmakers for Most.
His junior partner in government, the Most-Hid (Bridge) group, had demanded he dismiss Mr Kalinak, a founding member of his Smer party, by Monday.More news: Google celebrated Pi Day with special Doodle
Kalinak said he hoped that by resigning, "I will contribute to the stabilization of the situation in Slovakia".
"We have voted unanimously, if we come to agreement on early elections, our ministers will remain on their posts", Bugar said.
"We believe that only early elections would solve this situation", Bugar said after a meeting of his party's leadership that took nearly eight hours.
An global team of journalists has been formed to complete Kuciak's story.More news: The Raspberry Pi 3 Model B+ microcomputer promises more speed
- 3 reasons Rams should consider signing Jordy Nelson following release
- China congratulates Nepal President Bhandari on re-election
- Wenger: 'Lacazette out for Milan'
- Carlos Hyde to sign with Cleveland Browns
- Milenina leads Russian medal haul in PyeongChang with cross-country sprint gold
- Evacuations ordered ahead of next Southern California storm
- Ex-President Lee Faces Questioning in Corruption Probe
- Miley Cyrus Is Being Sued Over Her 2013 Single 'We Can't Stop'
- Exxon Mobil (XOM) Receiving Somewhat Favorable Media Coverage, Study Finds
- Sacking of JK Finance Minister Haseeb Drabu signals hard posturing by PDP