BRATISLAVA, Slovakia — Tens of thousands rallied across Slovakia on Thursday in a new wave of anti-government protests amid a political crisis triggered by the slayings of an investigative reporter and his fiancee.

The protesters in the capital and two dozen other towns and cities were demanding a thorough and independent investigation into the Feb.21 shooting deaths of Jan Kuciak and Martina Kusnirova.

"Let's not forget our first and key demand," organizer Juraj Seliga told the crowd at a packed downtown square in the capital of Bratislava after observing a minute of silence to honor the two.

Prime Minister Robert Fico's three-party coalition stepped down following large street protests sparked by the slayings. Kuciak was investigating possible widespread government corruption.

Prosecutors said that circumstances in the deaths suggested it was a contract killing.

President Andrej Kiska swore in a new Cabinet comprised of the same three parties in Fico's government and led by Peter Pellegrini, previously the deputy prime minister.

Many in Slovakia think the changes have not gone far enough.

The demonstrators particularly expressed their distrust in the national police chief, Tibor Gaspar, and want him replaced, something Kiska has also supported.