BRATISLAVA, Slovakia — Trying to maintain its grip on power, Slovakia’s governing party announced on Monday that the interior minister would step down, and pledged a thorough investigation into the killing of a young journalist who was investigating government corruption in the small Central European nation.

It was unclear whether the moves would be enough to salvage the government of Prime Minister Robert Fico and his party, SMER-SD, coming days after tens of thousands of people took to the streets, many of them calling for Mr. Fico to resign.

His coalition partner, the party Most-Hid, had demanded the resignation of the interior minister, Robert Kalinak, who oversees the police and was widely seen as an impediment to a thorough investigation into the killing. President Andrej Kiska has said that there are only two ways out of the crisis: a deep reconstruction of the government, or early elections.

Mr. Kalinak, speaking at a news conference Monday morning, acknowledged the governing party’s precarious hold on government.