"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: Pi Day deals: Blaze Pizza, Papa Murphy's, Boston Market, more
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: Sacking of JK Finance Minister Haseeb Drabu signals hard posturing by PDP
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: Teachers back walkout protesting gun violence
- The Raspberry Pi 3 Model B+ microcomputer promises more speed
- Carlos Hyde to sign with Cleveland Browns
- Exxon Mobil (XOM) Receiving Somewhat Favorable Media Coverage, Study Finds
- YouTube to display Wikipedia 'facts' alongside conspiracy videos
- Keenum Preparing to Sign with Denver
- Trump looks 'very strongly' at Larry Kudlow for chief economic adviser
- Ravens Not To Pick Up Option For RT Howard, Release RB Woodhead
- Wenger: 'Lacazette out for Milan'
- New Splinter Cell Game Spotted on Amazon Ahead of Announcement
- E3 2018 will be Xbox's 'Biggest Showing Ever' says Microsoft