Slovakia's interior minister will resign to prevent the collapse of Prime Minister Robert Fico's government, which is trying to fend off calls for early elections following the murder of an investigative journalist.
His is the third resignation in a matter of weeks.
Slovak investigative journalist Jan Kuciak and his fiancee were killed in their home last month.
The protests on Friday included calls for Slovakia's whole government to step down, with a particular focus on Kalinak and the head of the national police force.
President Andrej Kiska also has proposed early elections or substantial changes in the government as a way out of the crisis.
Kuciak's last article, which was published posthumously, revealed business links between political figures who are close to Mr Fico and Italian businessmen in Slovakia who are allegedly connected to the Calabria-based 'Ndrangheta Mafia group.
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The week before, Maria Troskova, the prime minister's chief state adviser, and Viliam Jasan, the secretary of the state security council, quit amid allegations about past dealings with the man. In case the government does not give its consent for the elections, the party plans to leave the coalition which, most probably, will result in early termination of the parliament's office.
Critics had claimed Mr Kalinak could not ensure an impartial investigation into the murders, in his role as overseer of the police.
"I think to fulfill my mandate, I have to do everything to preserve stability in Slovakia", Kalinak told reporters in Bratislava.
"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.
Before Most-Hid announced its demand, Fico still seemed intent on continuing the coalition government.