Slovakia's Interior Minister Robert Kalinak has resigned amid a political scandal caused by the murder of a journalist and his fiancée.
Prime Minister Robert Fico is fighting to keep his government together after Mr Kalinak bowed to pressure from a coalition partner, the Most-Hid party.
Another coalition party called for elections should Mr Fico lose Most-Hid's support.
Jan Kuciak was investigating government corruption when he was killed.
His fiancée, Martina Kusnirova, was also murdered.
The killings have gripped Slovakia, leading to calls for an investigation and anti-government protests in Bratislava on Friday which were thought to be the largest in the country since the fall of communism in 1989.
Slovakia in shock
Mr Kuciak had been working on a piece linking high-level political corruption in Slovakia with Italian mafia before he was killed.
Kuciak claimed that Italian businessmen with links to the Calabrian organised crime syndicate 'Ndrangheta had settled in eastern Slovakia, and had spent years embezzling EU funds.
Slovakia's President Andrej Kiska called for a "radical reconstruction" of the government or fresh elections last week to restore public faith, after all seven suspects arrested in connection with the murders were released without charge.
One of the men released was an Italian who had done business deals with officials close to Mr Fico.
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 a joint statement, the pair denied wrongdoing. They said they were stepping down during the investigation so their names would not be used in a political battle against Mr Fico.
Mr Fico hit back at the president, saying any changes would depend on his party, Smer-SD, and its two coalition partners.
"We won't dance on the graves of two young people, unlike opposition, media and, now, the president," he said.
However, Mr Fico's junior coalition partner, the Most-Hid group, demanded the resignation of Mr Kalinak in exchange for continued support of Smer-SD.
Critics had claimed Mr Kalinak could not ensure an impartial investigation into the murders, in his role as overseer of the police.
"It's important for stability to be maintained," Mr Kalinak told reporters as he announced his resignation as both interior minister and deputy PM.
Most-Hid welcomed Mr Kalinak's decision to step down, although the party did not indicate whether it would be enough for the coalition to maintain its support.
"The national council always decides," leader Bela Bugar told reporters, saying the group has "the final word" in such circumstances.
The party's leadership plans to meet later on Monday.
The third party in the coalition, the Slovak National Party, announced after the resignation that they would want early elections should Most-Hid stop supporting Mr Fico, or if Mr Fico lost his majority in parliament.